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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. - Mathematics and Statistics

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Sum

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`

Concept: Conditional Probability
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