Answer:
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)](https://img.qammunity.org/2022/formulas/mathematics/college/omnibtgvur9vdm50rvd627fz01ha1ay6di.png)
In which
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)!)](https://img.qammunity.org/2022/formulas/mathematics/college/mztppiaohythui2rvvokdfm636pzgsn6x6.png)
And p is the probability of X happening.
Five trials, probability of a success is 50%.
This means that
![n = 5, p = 0.5](https://img.qammunity.org/2022/formulas/mathematics/college/6sxdvolmietxvvc5v22301dcqctesh9huw.png)
Probability of exactly two successes
This is P(X = 2). So
![P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)](https://img.qammunity.org/2022/formulas/mathematics/college/omnibtgvur9vdm50rvd627fz01ha1ay6di.png)
![P(X = 2) = C_(5,2).(0.5)^(2).(0.5)^(3) = 0.313](https://img.qammunity.org/2022/formulas/mathematics/college/wsay2e6vc9tyqxn81uhvfmiwu1wt2m6f65.png)
0.313*100% = 31.3%