Answer to Question #276456 in Statistics and Probability for D536

Question

Based on a​ poll, 60​% of adults believe in reincarnation. Assume that 6 adults are randomly​ selected, and find the indicated probability. What is the probability that all of the selected adults believe in​ reincarnation?

Answer 1

$p=0.6 \\ q = 1-p = 1 -0.6 = 0.4 \\ n= 6$

Using Binomial distribution

$P(X=x) = \binom{n}{x}p^xq^{n-x} \\ P(X=6) = \binom{6}{6} \times 0.6^6 \times 0.4^{6-6} \\ = 1 \times 0.6^6 \times 1 \\ = 0.046656$