Lesson Challenging problems on Binomial distribution probability
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<H2>Challenging problems on Binomial distribution probability</H2> <H3>Problem 1</H3>Let X represents the difference between the number of heads and the number of tails when a coin is tossed 33 times. Find P (X=3). <B>Solution</B> <pre> In this problem, the sum Heads+Tails is 33, while the difference Heads-Tails = 3. It immediately implies that Heads = 18, Tails = 15. Therefore, the event X= 3 is EQUIVALENT to event Tails = 15. Now, P(Tails=15) is (use the formula of probability for the Binomial distribution) P(Tails=15) = {{{C[33]^15*(1/2)^15*(1/2)^18}}} = BIMON.DIST(15, 33, 0.5, FALSE) = 0.120741. <U>ANSWER</U> I used the standard EXCEL function to calculate the binomial distribution probability. Its first parameter is the "number of successful trials" (k= 15 in this case). Its second parameter is the "number of trials n" (n= 33 in this case). Its third parameter is "the probability of success in each one single trial" (p= 0.5 in this case); and The fourth parameter says if you want calculate a single addend or the sum of addends (the single addend in this case). Input "=BINOM.DIST(15, 33, 0.5, FALSE)" into any MS Excel cell in your computer and press enter to get the answer P = 0.120741 immediately. On Excel function BINOM.DIST, see its description everywhere, for example https://support.office.com/en-us/article/binom-dist-function-c5ae37b6-f39c-4be2-94c2-509a1480770c </pre> <H3>Problem 2</H3>A person flips a coin to determine whether she's moving forwards or backward. If she flips a head, she moves 1 step forward, and if she flips a tail, she moves 1 step backward. What is the probability that after 4 coin tosses, she will be in the same place? <B>Solution</B> <pre> It is the probability of getting two tails and two heads of 4 flips in any order P(2T2H of 4) = {{{C[4]^2*(1/2)^2*(1/2)^2}}} = {{{((4*3)/(1*2))*(1/2)^4}}} = 0.375. <U>ANSWER</U> </pre> My other Additional lessons on Probability in this site are - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Sample-space-conception-problems-REVISITED.lesson>Sample space conception problems REVISITED</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-probability-problems-using-complementary-probability-REVISITED.lesson>Solving probability problems using complementary probability REVISITED</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Elementary-Probability-problems-related-to-combinations-REVISITED.lesson>Elementary Probability problems related to combinations REVISITED</A> - <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/More-conditional-probability-problems.lesson>Conditional probability problems REVISITED</A> - 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