Question

It is known that for students who studied English for at least 50 hours, their chance of passing the quiz is 0.95, while for those who studied English for less than 50 hours, their chance of passing the quiz is 0.1. It is also known that the probability of passing the quiz is 90%. If a student is randomly chosen and is found to have passed the quiz, what is the probability that he has studied for less than 50 hours?

Answer #1

Solution: Given information ,

A : at least 50 hours , B : less than 50 hours , C : passed the quiz

p( at least 50 hours and passed the quiz) = P(A and C) = 0.95

p( less than 50 hours and passed the quiz) = P( B and C) = 0.10

p(passing the quiz) = P(C) = 0.90

Hence, Using Condition probability formula,

P( less than 50 hours given passed the quiz) = P( less than 50 hours and passed the quiz) / P(pass the quiz)

= P( B and C) / P(C)

= 0.10 / 0.90

= 0.1111

Answer : **0.1111**

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