Answer :
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.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinatios of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
In this problem
There are 5 adults, so [tex]n = 5[/tex]
60% believe in reincarnation, so [tex]p = 0.6[/tex]
What is the probability that exactly 4 of the selected adults believe in reincarnation?
This is P(X = 4).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{5,4}.(0.6)^{4}.(0.4)^{1} = 0.2592[/tex]
There is a 25.92% probability that exactly 4 of the selected adults believe in reincarnation.