Probability=0.3423

Step-by-step explanation

This is a binomial distribution problem because the probability is is mutually exclusive and independent of each other, the formula for it is:

Probability=(xn?)⋅px⋅qn−x

 

(xn?)canbewrittenasr!(n−r)!n!?

 

where:

n = number of trials

x = number of times for a specific outcome within n trials

p = probability of success in a single trial

q = probability of failure in a single trial

   = 1 - p

 

Based on the question, we are given:

n = 5

x = 2

p = 37 % or 0.37

q = 1 - 0.37  = 0.63

 

It is stated in the problem, that we need exactly two so x = 2, now let us substitute the given values in the formula:

Probability=(xn?)⋅px⋅qn−x

Probability=(25?)⋅0.372⋅0.635−2

Probability=2!(5−2)!5!?⋅0.372⋅0.635−2

Probability=2!(5−2)!5!?⋅0.372⋅0.633

Probability=10⋅0.1369⋅0.250047

Probability=0.3423

 

I hope I helped you understand this topic. If I have a lack of answers or you need more explanation please comment in the comment section. Thank you so much!