Question

Find the probability of exactly two

successes in five trials of a binomial
experiment in which the probability of
success is 50%.

Round to the nearest tenth of a
percent.

[? ]%

Answer 1

31.3%

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) = (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%