Question 196915
1. A die is rolled 5 times. Find the probability that:
a) exactly 2 threes are thrown 
# of ways to select two places from the five: 5C2 = (5*4)/(1*2) = 10
P(getting a 3) = 1/6
P(not getting a 3) = 5/6
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P(2 threes if a die is tossed 5 times) = 10(1/6)^2(5/6)^3 = 0.1608
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b) No more than 2 fives are thrown
P(0,1, or 2 5's in 5 throws) = 0.9645
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c) Between 1 and 4 are thrown
P(1,2,3 or 4 in 5 throws) = 0.5980
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2. A Box Contains 5 White (W) and 4 Black (B) marbles. 
3 marbles are drawn without replacement. 
Find the following:
a) P (2 W / 1st B) = [5C2*4C1]/[9C3] = 0.4762
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b) P (At least 1W / 1st B)
What do you mean by "1st B"?
Is this supposed to be a conditional statement?
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d) P (W / 1St and 2Nd B), but this time, assume replacement.
That's confusing.
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2. Assume 8 distinctly title books: 2 green, 3 brown, 1 red, 1 blue, and 1 yellow.
a) Looking only at titles, how many ways can these 8 books be arranged on a shelf?
Ans 8! = 40320
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b) Looking only at titles, how many ways can 5 of 8 books be arranged on a shelf?
Ans: 8P5 = 6720
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c) Looking only at color, how many ways can these 8 books be arrange on a shelf?
Ans: 5! = 120
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d) Looking only at titles, how many ways can we choose 5 books to read?
Ans: 8C5 = 56
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e) How many ways can we choose 2 brown books to read?
Ans: 3C2 = 3
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f) Looking only at color, what is the probability that we choose 2 green books to read? 
Ans: 2C2/8C2 = 1/28
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Cheers,
Stan H.