If 30% of people taking an exam fail and 3 people take the exam what is the probability one will fail?

Question

I need to know what the probability is one person fails out of three taking an exam when the percentage of failure is 30%. 

Answer 1

The probability that at least one will fail is easy to work out.   It is  1 - (.7)³  = .657   This the complement of the probability that all three pass ( prob = .7³  ).   

 

Computation of the probability that exactly one will fail is harder.   There are three ways this can happen (the first student fails and the other two pass, the second student fails and the other two pass, or the third student fails and the other two pass).  The probability of each of these is   (.3) (.7)²  =  .147, so three times this is .441  

 

This problem is an example application of the binomial distribution.