Answer to Question #342827 in Statistics and Probability for ton

Question #342827
  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.
1
Expert's answer
2022-05-20T04:43:30-0400

"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\\%"

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