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Question
In an examination, 30% of students have failed in subject I, 20% of the students have failed in subject II and 10% have failed in both subject I and subject II. A student is selected at random, what is the probability that the student has failed in subject I, if it is known that he is failed in subject II?
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Solution
Let A be the event that the student failed in Subject I
B be the event that the student failed in Subject II
Then P(A) = 30% = `30/100`
P(B) = 20% = `20/100`
And P(A ∩ B) = 10% = `10/100 `
P (student failed in Subject I, given that he has failed in Subject II)
= `"P"("A"/"B") = ("P"("A" ∩ "B"))/("P"("B")`
= `({10/100})/({20/100})`
= `10/20`
= `1/2`
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