Answer to Question #342827 in Statistics and Probability for ton

Question

1. If a student randomly guesses at five multiple-choice questions, find the probability that the student gets exactly three correct. Each question has five possible choices.

Answer 1

$P(x)=\frac {n!} {(n-x)!x!}p^xq^{n-x}$

where $n=5, p=1/5,q=1-p=4/5$

So,

$P(3)=\frac {5!} {(5-3)!3!}(\frac 1 5)^3(\frac 4 5 )^{5-3}=0.08*0.64=0.0512=5.12\%$