Statistics Question

Question

Based on a pole 60% of adults believe in reincarnations assume that six adults are randomly selected and find the indicated probability. Part a. What is the probability that exactly 4 of the 5 selected adults believe in reincarnation is?

Answer 1

This is a binomial distribution, since there are exactly two alternatives with known probabilities.

p = .60 (60%), q = 1 - p = .40.

The probability that exactly 4 out of 5 selected adults is the number of ways of selecting 4 out of 5 adults, which can be written 5C4 (which can be read as "5 choose 4"), multiplied by the probability the probability that each of these 4 adults believes in reincarnation p^4 = .60^4, multiplied by the probability that the remaining 1 adult does not believe in reincarnation (1-p)^1 = .40^1.

So the complete answer can be calculated as 5C4 * .60^4 * .40^1

Numerically, 5C4 = 5, .60^4 = .1296, .40^1 = .40

So the product of these is .2592

The general formula for the probability of the result of n independent trials resulting in exactly k "successes" when the probability of success in any single trial is p, is given by

nCk p^k (1-p)^(n-k)

As an aside, the above answer can be checked on wolframalpha.com by entering

(5 choose 4) * (.6)^4 * (.4)^1