GATE ME 2015 Set 2 — Question 36
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Engineering Mathematics → Probability → Conditional Probability
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Question
The chance of a student passing an exam is 20%. The chance of a student passing the exam and getting above 90% marks in it is 5%. GIVEN that a student passes the examination, the probability that the student gets above 90% marks is
Correct answer
(B) (1)/(4)
Solution
This is a problem of conditional probability. Let
Let
The probability that a student passes AND gets above 90% marks is .We are asked to find the probability that a student gets above 90% marks GIVEN that they passed the exam, which is .Using the formula for conditional probability:
Thus, the correct option is (B).
P(A) be the probability that a student passes the exam. Given .Let
P(B) be the probability that a student gets above 90% marks.The probability that a student passes AND gets above 90% marks is .We are asked to find the probability that a student gets above 90% marks GIVEN that they passed the exam, which is .Using the formula for conditional probability:
Thus, the correct option is (B).
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