SOLUTION: A business organization needs to make up a 5 member fund-raising committee. The organization has 10 accounting majors and 8 finance majors. What is the probability that at most 2

Question 959516: A business organization needs to make up a 5 member fund-raising committee. The organization has 10 accounting majors and 8 finance majors. What is the probability that at most 2 accounting majors are on the committee? really lost on this need help
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
It is necessary to consider, in addition to the given probability(P), all probabilities smaller than the given probability ("at most").
P(at most 2 accounting majors on the committee) = P(0) + P(1) +P(2)
We use the following formula for binomial probability to calculate the above P's
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P = combination of n things taken r at a time * P^r * Q^(n-r), where n is number of trials, r is number of specific events you wish to obtain, P = probability that the event will occur, Q is probability that the event will not occur (Q = 1 - P, the complement of the event)
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P(0) = ( 5! / (0! * 5!) ) * (10/18)^0 * (8/18)^5 = 0.01734153
note that n = 5 (size of the committee)
P(1) = ( 5! / (1! * 4!) ) * (10/18)^1 * (8/18)^4 = 0.108384562
P(2) = ( 5! / (2! * 3!) ) * (10/18)^2 * (8/18)^3 = 0.270961405
P(0) + P(1) + p(2) = 0.01734153 + 0.108384562 + 0.270961405 = 0.396687497
The rounded total is 0.40 probability for at most 2 accounting majors on the committee

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