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Recent problems solved by 'stanbon'

stanbon answered: 57911 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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Radicals/599849: How do you simplify √12 + 6√3 +2√6? Can you show the step by step process? Thank you!(: 1 solutions Answer 379120 by stanbon(57984)   on 2012-04-16 21:46:37 (Show Source): You can put this solution on YOUR website! √12 + 6√3 +2√6 ----------- = sqrt(4)*sqrt(3) + 6*sqrt(3) + 2*sqrt(2)*sqrt(3) ------ Factor out the sqrt(3): ---- = (2 + 6 + sqrt(2))*sqrt(3) ------ = (8+sqrt(2))*sqrt(3) ========================= Cheers, Stan H.

Radicals/599858: How do you simplify √(75m^2np^4)? Can you show the step by step process? Thank you!(: 1 solutions Answer 379119 by stanbon(57984)   on 2012-04-16 21:43:06 (Show Source): You can put this solution on YOUR website! √(75m^2np^4)? -------------------- = sqrt(25m^2p^4)*sqrt(3) ---- = 5mp^2*sqrt(3) ================== Cheers, Stan H.

Age_Word_Problems/599852: I am 30 years old and my sister is 10. I need an equation to figure out how old my sister and I will be when I am three times as old as my sister. 1 solutions Answer 379118 by stanbon(57984)   on 2012-04-16 21:41:03 (Show Source): You can put this solution on YOUR website! I am 30 years old and my sister is 10. I need an equation to figure out how old my sister and I will be when I am three times as old as my sister. ---- You are now 3 times as old as old as your sister. That will never happen at a later or earlier age. ----- Maybe you would like to know whan you will be 5 times as old as your sister. Equation: (30+x) = 5(10+x) 30+x = 50 + 5x 4x = -20 x = -5 ---- When you are 30-5 = 25 you will be 5 times as old as your sister, who will be 10-5 = 5... So that happened in the past; and it will never happen again. Cheers, Stan H.

Volume/599848: Hi, I need help as soon as possible with a question about areas and volumes of similar solids. Im not even sure how to start out, because the examples aren't helping me much. So here's the question: A cylinder 4 in. in diameter and 6 in. high holds 1 lb of oatmeal. To the nearest ounce, how much oatmeal will a similar 10 in. high cylinder hold?(hint: 1 lb = 16 oz) First, I tried to put the numbers in proportions such as 4 over the unknown diameter, and 6 in. over 10 in. to find the unknown diameter. The answer I got was 6.6666 and so on, but Im not sure if Im supposed to leave it like that, round it, or leave it as a mixed fraction. After that, how do I calculate how much oatmeal is in the higher cylinder? I would like it if it can be explained to me clearly because this kind of problem confuses me. I really hope someone can help me soon on this problem. Thank you! 1 solutions Answer 379111 by stanbon(57984)   on 2012-04-16 21:32:27 (Show Source): You can put this solution on YOUR website! A cylinder 4 in. in diameter and 6 in. high holds 1 lb of oatmeal. To the nearest ounce, how much oatmeal will a similar 10 in. high cylinder hold?(hint: 1 lb = 16 oz) ------------- Volume of the cylinder: Base*height = (pi)r^2*h = 16(pi)*6 = 96(pi) cubic inches. ------- Note: That volume holds 1 lb of oatmeal. ---------- how much oatmeal will a similar 10 in. high cylinder hold?(hint: 1 lb = 16 oz) Volume = 16(pi)*10 = 160(pi) cu inches ------- # of lbs. of oatmeal in the larger cylinder = [160(pi)]/(96(pi)) = 1 2/3 lbs = 1 lb 10 2/3 ounces ===================================== Cheers, Stan H.

Probability-and-statistics/599845: Textbook authors and publishers work very hard to minimize the number of errors in a textbook. However, some errors are unavoidable. Mr. J. A. Carmen, statistics editor, reports that the mean number of errors per chapter is 0.8. What is the probability that there are less than 2 errors in a particular chapter? 1 solutions Answer 379109 by stanbon(57984)   on 2012-04-16 21:23:44 (Show Source): You can put this solution on YOUR website! What is the standard deviation of the distribution?

Inequalities/599843: -y>2x 1 solutions Answer 379107 by stanbon(57984)   on 2012-04-16 21:21:02 (Show Source): You can put this solution on YOUR website! -y>2x --- Solve for "y": y < -2x ============== =============================================== Cheers, Stan H.

logarithm/599824: a. rewrite the expression in terms of log x and log y. log(x^4y^3) B. rewrite the expression as a single log. 2Inx+5Inz 1 solutions Answer 379099 by stanbon(57984)   on 2012-04-16 21:04:34 (Show Source): You can put this solution on YOUR website! a. rewrite the expression in terms of log x and log y. log(x^4y^3) = log(x^4) + log(y^3) = 4log(x) + 3log(y) -------------------------------------------------------------- b. rewrite the expression as a single log. 2Inx+5Inz --- = 7ln(x) OR = ln(x^7) ============== Cheers, Stan H.

Quadratic_Equations/599830: Not understanding what I need to compare: question is. Compare the graph of each function: F(x)=x^2 g(x)=5x^2+10 1 solutions Answer 379098 by stanbon(57984)   on 2012-04-16 20:58:34 (Show Source): You can put this solution on YOUR website! Not understanding what I need to compare: question is. Compare the graph of each function: F(x)=x^2 g(x)=5x^2+10 ------ F and g are the same basic graph --- g has a sharper fall and rise then F All the points of g are then raised higher by 10 ================== =================== cheers, Stan H.

Age_Word_Problems/599805: In one day, Frank's family drove for 11hr. Each hour they average 65 miles, How many miles did they drive that day? this one is 11x65=615, I GOT THIS PART What I need help with is: show your multiplication by breaking apart 65 to 60 and 5 1 solutions Answer 379089 by stanbon(57984)   on 2012-04-16 20:10:17 (Show Source): You can put this solution on YOUR website! show your multiplication by breaking apart 65 to 60 and 5 ------------------- 11*65 = 11*(60+5) = 11*60 + 11*5 = 660 + 55 = 715 ============= Cheers, Stan H.

Probability-and-statistics/599699: 2. There is adequate information in each of the following to decide whether to reject or fail to reject the null hypothesis. Carefully examine the statements; you should not have to perform any computations. What is your decision and explain why. a) Ho: μ = 120 Let α = 0.05. Data: x̅ = 130.1 for n = 100, P-value = 0.068 H1: μ ≠ 120 b) Ho: σ = 2.8 Let α = 0.01. Data: s = 3.1 for n = 55 H1: σ < 2.8 c) Ho: p = 0.68 Let α = 0.05. Data: p̂ = 0.69 for n = 32, test statistic z = 0.09095 H1: p > 0.68 1 solutions Answer 379076 by stanbon(57984)   on 2012-04-16 19:28:23 (Show Source): You can put this solution on YOUR website! 2. There is adequate information in each of the following to decide whether to reject or fail to reject the null hypothesis. Carefully examine the statements; you should not have to perform any computations. What is your decision and explain why. a) Ho: μ = 120 Let α = 0.05. Data: x̅ = 130.1 for n = 100, P-value = 0.068 H1: μ ≠ 120 ---- Ans: p-value is greater than 5% so fail reject Ho. ------------------------------------------------------------ b) Ho: σ = 2.8 Let α = 0.01. Data: s = 3.1 for n = 55 H1: σ < 2.8 Ans: No decision as cannot determine test statistic or p-value --------------------------------------------------------------- c) Ho: p = 0.68 Let α = 0.05. Data: p̂ = 0.69 for n = 32, test statistic z = 0.09095 H1: p > 0.68 p-value = P(z > 0.09095) = normalcdf(0.09095,100) = 0.4638 --- Since the p-value is greater than 5%, fail to reject Ho. ==================== Cheerd, Stan H.

Probability-and-statistics/599706: Perform a hypothesis test for the following problem. Use the same format as the hypothesis test worksheets. An office building complex uses thousands of fluorescent light bulbs each year. The brand of bulb it currently uses has a mean life of 900 hours. A manufacturer claims that its new brand of bulbs, which cost the same as the brand the complex currently uses, has a mean life of more than 900 hours. The office building’s management has decided to purchase the new brand if, when tested, the evidence supports the manufacture’s claim at the 0.05 significance level. Suppose 64 bulbs were tested with the following results: x̅ = 920 hours, s = 80 hours. Will the office building management purchase the new brand of fluorescent bulbs? 1 solutions Answer 379072 by stanbon(57984)   on 2012-04-16 19:21:18 (Show Source): You can put this solution on YOUR website! An office building complex uses thousands of fluorescent light bulbs each year. The brand of bulb it currently uses has a mean life of 900 hours. A manufacturer claims that its new brand of bulbs, which cost the same as the brand the complex currently uses, has a mean life of more than 900 hours. The office building’s management has decided to purchase the new brand if, when tested, the evidence supports the manufacture’s claim at the 0.05 significance level. Suppose 64 bulbs were tested with the following results: x̅ = 920 hours, s = 80 hours. Will the office building management purchase the new brand of fluorescent bulbs? ----------------- Ho: u <= 900 Ha: u > 900 (claim) ----- x-bar = 920 --- z(920) = (920-900)/[80/sqrt(64)] = 20/[10) = 2 --- p-value = P(z > 2) = normalcdf(2,100) = 0.0228 ---- Since the p-value is less than 5%, reject Ho. The test results support the claim. =============== Cheers, Stan H.

Exponential-and-logarithmic-functions/599767: (log x)^2=log x^2 1 solutions Answer 379071 by stanbon(57984)   on 2012-04-16 19:14:00 (Show Source): You can put this solution on YOUR website! (log x)^2=log x^2 ----- (log(x)^2 - 2log(x) = 0 ------ Factor: (log(x))[log(x) - 2] = 0 --- log(x) = 0 or log(x) = 2 ---- x = 10^0 or x = 10^2 x = 1 or x = 100 ===================== Cheers, Stan H.

test/599777: log_5 (x^2/625y^5) 1 solutions Answer 379068 by stanbon(57984)   on 2012-04-16 19:09:54 (Show Source): You can put this solution on YOUR website! log_5 (x^2/625y^5) ------------ = log5(x^2) - [log(625)+log5(y^5)] ------ = log5(x^2) - [4 + 5log5(y)] ================================= Cheers, Stan H. =============

Probability-and-statistics/599773: An arcade has 20 different arcade games. You want to play at least 14 of them. How many different combinations of arcade games can you play? 1 solutions Answer 379066 by stanbon(57984)   on 2012-04-16 19:05:12 (Show Source): You can put this solution on YOUR website! An arcade has 20 different arcade games. You want to play at least 14 of them. How many different combinations of arcade games can you play? ---------------------- Ans: 20C14 = 20C6 = (20*19*18*17*16*15)/(1*2*3*4*5*6) = 39760 ======================= Cheers, Stan H.

Exponential-and-logarithmic-functions/599772: log7(3-4x)=log7(x/3) 1 solutions Answer 379063 by stanbon(57984)   on 2012-04-16 18:58:08 (Show Source): You can put this solution on YOUR website! log7(3-4x)=log7(x/3) ----------------- 3-4x = x/3 4x + (x/3) = 3 12x + x = 9 13x = 9 x = 9/13 ------------- Cheers, Stan H.

Trigonometry-basics/599738: show an evaluatuion of sin 120 degrees uaing the trigonometric addidtion formulas 1 solutions Answer 379054 by stanbon(57984)   on 2012-04-16 18:28:10 (Show Source): You can put this solution on YOUR website! show an evaluatuion of sin 120 degrees uaing the trigonometric addidtion formulas ----- sin(120) = sin(90+30) = sin(90)cos(30) + cos(90)*sin(30) ------- = 1*cos(30) + 0*(1/2) ----- = cos(30) = sqrt(30)/2 ============================= Cheers, Stan H.

Polynomials-and-rational-expressions/599742: What is the factor to b squared + 16b + 63 ? 1 solutions Answer 379053 by stanbon(57984)   on 2012-04-16 18:23:00 (Show Source): You can put this solution on YOUR website! What is the factor to b squared + 16b + 63 ? -------- b^2 + 16b + 63 ---- (b+9)(b+7) ============== Cheers, Stan H.

Trigonometry-basics/599733: solve for data such that 0 degrees the less than data less than 360 1 solutions Answer 379051 by stanbon(57984)   on 2012-04-16 18:19:42 (Show Source): You can put this solution on YOUR website! confusing

test/599591: Jim and Wanda both have some apples. If Jim gives Wanda an apple, they will both have the same number of apples. However, if Wanda gives Jim an apple, Jim will have twice as many as Wanda. How many apples does Jim have and how many apples does Wanda have? 1 solutions Answer 379014 by stanbon(57984)   on 2012-04-16 13:03:15 (Show Source): You can put this solution on YOUR website! Jim and Wanda both have some apples. If Jim gives Wanda an apple, they will both have the same number of apples. However, if Wanda gives Jim an apple, Jim will have twice as many as Wanda. How many apples does Jim have and how many apples does Wanda have? ------- Equations: j-1 = w+1 j = 2(w-1) ------ Substitute for "j" and solve for "w": 2(w-1) - 1 = w + 1 2w-2 -1 = w+1 2w-3 = w+1 w = 4 (Wanda has 4 apples) ---- solve for "j": j = 2(w-1) j = 2(3) = 6 (Jim has 6 apples). --------------------------- Cheers, Stan H. =============

Angles/599587: In a certain triangle the measure of the medium-sized angle is three times the measure of the smallest angle and half the measure of the largest angle. What are the measurements of the three angles? 1 solutions Answer 379013 by stanbon(57984)   on 2012-04-16 12:58:43 (Show Source): You can put this solution on YOUR website! In a certain triangle the measure of the medium-sized angle is three times the measure of the smallest angle and half the measure of the largest angle. What are the measurements of the three angles? ------- smallest angle: x median-sized angle: 3x largest angle: 6x ---- Equation: x + 3x + 6x = 180 degrees 10x = 180 x = 18 degrees 3x = 54 degrees 6x = 108 degrees ==================== Cheers, Stan H.

expressions/599585: I am returning adult student to college, and would like to refresh my memory. How can I simplify 5x2-(2+13)/3+2-5+6. Any help would be gladly appreciated. 1 solutions Answer 379012 by stanbon(57984)   on 2012-04-16 12:54:56 (Show Source): You can put this solution on YOUR website! simplify 5x2-(2+13)/3+2-5+6. ------ = 5x^2-(15)/3 + 8-5 ------- = 5x^2 - 5 + 8 -5 ------- = 5x^2 -2 =============== Cheers, Stan H.

Coordinate-system/599586: what is the slope of the line given by the equation below ? y = 6x 1 solutions Answer 379011 by stanbon(57984)   on 2012-04-16 12:51:17 (Show Source): You can put this solution on YOUR website! what is the slope of the line given by the equation below ? y = 6x ---- The slope is the amount y changes when x changes by 1. If x = 0, y = 6*0 = 0 If x = 1, y = 6*1 = 6 ------ So the slope = 6 =============== Cheers, Stan H.

Rational-functions/599578: Given that f(x)=x/1-x^2 , g(x)=1/x . how to find fog (x) and gof(x) ...and how find the domains of composite functions. 1 solutions Answer 379010 by stanbon(57984)   on 2012-04-16 12:50:10 (Show Source): You can put this solution on YOUR website! Given that f(x)=x/1-x^2 , g(x)=1/x . how to find fog (x) and gof(x) ...and how find the domains of composite functions. ---- gof(x) = g[f(x)] = g[x/(1-x^2)] ==== = (1-x^2)/x --- Domain: All Real Numbers except -1,0, and +1 ========================== Cheers, Stan H.

Probability-and-statistics/599535: if the correlation between age and physial flexibility is -68 what does this mean? How would this correlation look on a scatter diagram? What general shape would it have? 1 solutions Answer 379000 by stanbon(57984)   on 2012-04-16 10:53:23 (Show Source): You can put this solution on YOUR website! if the correlation between age and physial flexibility is -68 what does this mean? How would this correlation look on a scatter diagram? What general shape would it have?----- ---- -0.68 implies a decent level of negative linear correlation in the data. ------ Looks ?: As the age values increase the flecibility numbers decrease. --- Looks: Data slants downward as you scan to the right. ---- Cheers, Stan H.

Probability-and-statistics/599532: it is thought that a normal population's mean is less than 75. To test this, a random sample of size 19 is drawn. THe sample mean is 73.5 and the sample standard deviation is 2.1. Find an approximate range for the p-value and state the conclusion. What would your range be if we had used a two-tail test? 1 solutions Answer 378998 by stanbon(57984)   on 2012-04-16 10:48:43 (Show Source): You can put this solution on YOUR website! it is thought that a normal population's mean is less than 75. To test this, a random sample of size 19 is drawn. THe sample mean is 73.5 and the sample standard deviation is 2.1. Find an approximate range for the p-value and state the conclusion. What would your range be if we had used a two-tail test? ------ Ho: u >= 75 Ha: u < 75 (claim) ------ Test stat: t(73.5) = (73.5-75)/[2.1/sqrt(19)] = -3.1135 ----- p(value) = P(t < -3.1135 when df = 18) = 0.0030 Since the p-value is < 5%, reject Ho at the 5% significance level. ----- If a 2-tail test, p-value = 2*0.0030 = 0.0060 We would still reject Ho. ================== Note: The test results support the claim. ============================================ Cheers, Stan H.

Probability-and-statistics/599452: After a losing season, there is a great uproar to fire the head football coach. In a random sample of 250 college alumni, 105 favor keeping the coach. Test at the .01 level of significance whether the proportion of alumni who support the coach is less than 50 percent. State the null hypothesis and the alternate hypothesis State the decision rule for .01 significance level. Compute the value of the test statistic 1 solutions Answer 378996 by stanbon(57984)   on 2012-04-16 10:40:45 (Show Source): You can put this solution on YOUR website! After a losing season, there is a great uproar to fire the head football coach. In a random sample of 250 college alumni, 105 favor keeping the coach. Test at the .01 level of significance whether the proportion of alumni who support the coach is less than 50 percent. State the null hypothesis and the alternate hypothesis State the decision rule for .01 significance level. Compute the value of the test statistic ------------------------------ Ho: p >= 1/2 Ha: p < 0.5 (claim) ---- p-hat = 105/250 = 0.42 ---- Test statistic: z(0.42) = (0.42-0.5)/sqrt[0.5*0.5/250] = -2.5298 ------ p-value = P(z < -2.5298) = 0.0057 ---- Since the p-value is less than 1%, reject Ho. Conclusion: The test results support the claim. ==================== Cheers, Stan H. ====================

Probability-and-statistics/599522: Age Males Females 65-69 1.6 0.0 70-74 0.0 2.2 75-79 4.9 2.3 80-84 8.6 7.8 85+ 35.0 27.9 Prevalence of Alzheimer's disease (cases per 100 population) Suppose an unrelated 77 year old man, 76 year old woman, and 82 year old woman are selected from the community. What is the probability that all three of these individuals have Alzheimer’s? 1 solutions Answer 378995 by stanbon(57984)   on 2012-04-16 10:30:15 (Show Source): You can put this solution on YOUR website! Age Males Females 65-69 1.6 0.0 70-74 0.0 2.2 75-79 4.9 2.3 80-84 8.6 7.8 85+ 35.0 27.9 an Prevalence of Alzheimer's disease (cases per 100 population) Suppose an unrelated 77 year old man ::: 0.049 76 year old woman:: 0.023 82 year old woman : 0.078 are selected from the community. What is the probability that all three of these individuals have Alzheimer’s? Ans: 0.049*0.023*0.078 = 0.0000879 ==================== Cheers, Stan H.

Polynomials-and-rational-expressions/599527: Simplify. write your answers in the form of a+bi, where a and b are real numbers (7-(-36i)(2+(-100i) the -36 and -100 is in the inf 1 solutions Answer 378994 by stanbon(57984)   on 2012-04-16 10:22:40 (Show Source): You can put this solution on YOUR website! (7-(-36i)(2+(-100i) --- Use FOIL: F: 7*2 = 14 O:7*(-100i) = -700i I:2*(-36i) = -72i L:(-100i)(-36i) = -3600 -------------------- Combine to get: -3586 -736i ===================== Cheers, Stan H.

Sequences-and-series/599525: A playground is being designed where children can interact with their friends in certain combinations. If there is 1 child, there can be 0 interactions. If there are 2 children, there can be 6 interactions. If there are 3 children, there can be 15 interactions. If there are 4 children, there can be 27 interactions. How many interactions will there be for 7 children? 1 solutions Answer 378992 by stanbon(57984)   on 2012-04-16 10:18:49 (Show Source): You can put this solution on YOUR website! A playground is being designed where children can interact with their friends in certain combinations. If there is 1 child, there can be 0 interactions. If there are 2 children, there can be 6 interactions. If there are 3 children, there can be 15 interactions. If there are 4 children, there can be 27 interactions. How many interactions will there be for 7 children? --- I ran a Quadratic Regression program on the data and got the following formula: y = (3/2)x^2 + (3/2)x -3 --- f(7) = 81 ================= Cheers, Stan H.

Linear-equations/599526: what is an equation in slope intercept form that passes threw (13,9) and (30,26) 1 solutions Answer 378988 by stanbon(57984)   on 2012-04-16 10:12:21 (Show Source): You can put this solution on YOUR website! (13,9) and (30,26) ---- slope = (26-9)/(30-13) = 17/17 = 1 ---- Form: y = mx + b Solve for "b": 9 = 1*13 + b b = -4 ---- Equation: y = x -4 =================== Cheers, Stan H.

Probability-and-statistics/599423: Four cards are drawn without replacement from pack of cards . What is the probability that (a) they all are of different suit . (b) they all are aces. 1 solutions Answer 378940 by stanbon(57984)   on 2012-04-15 22:40:33 (Show Source): You can put this solution on YOUR website! Four cards are drawn without replacement from pack of cards . What is the probability that ( a) they all are of different suit. # of ways to succeed: 13*13*13*13 = 28561 # of random results: 52C4 = 270725 P(4 of different suit) = 13^4/52C4 = 0.1055 ------------------------------------ b) they all are aces. # of ways to succeed: 1 # of random results 52C4 --- P(4 aces) = 1/52C4 = 0.000003694 ==================================== Cheers, Stan H. ==============