Question

Find the probability of exactly two

Answer 1

Answer:

31.3%

Step-by-step explanation:

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 combinations 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.

Five trials, probability of a success is 50%.

This means that $n = 5, p = 0.5$

Probability of exactly two successes

This is P(X = 2). So

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

$P(X = 2) = C_{5,2}.(0.5)^{2}.(0.5)^{3} = 0.313$

0.313*100% = 31.3%