Question

Based on a​ poll, 60​% of adults believe in reincarnation. Assume that 5 adults are randomly​ selected, and find the indicated probability. What is the probability that exactly 4 of the selected adults believe in​ reincarnation?

Answer 1

Answer:

There is a 25.92% probability that exactly 4 of the selected adults believe in​ reincarnation.

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they believe in reincarnation, or they do not believe. This means that we can solve this problem using the binomial probability distribution.

Binomial probability distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem

There are 5 adults, so $n = 5$

60% believe in reincarnation, so $p = 0.6$

What is the probability that exactly 4 of the selected adults believe in​ reincarnation?

This is P(X = 4).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 4) = C_{5,4}.(0.6)^{4}.(0.4)^{1} = 0.2592$

There is a 25.92% probability that exactly 4 of the selected adults believe in​ reincarnation.