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Question
In a college, 30% students fail in physics, 25% fail in mathematics and 10% fail in both. One student is chosen at random. The probability that she fails in physics if she has failed in mathematics is ______.
Options
`1/10`
`2/5`
`9/20`
`1/3`
Solution
In a college, 30% students fail in physics, 25% fail in mathematics and 10% fail in both. One student is chosen at random. The probability that she fails in physics if she has failed in mathematics is `2/5`.
Explanation:
Let E1 be the event that the student fails in Physics and E2 be the event that she fails in Mathematics.
∴ P(E1) = `30/100`
P(E2) = `25/100`
And P(E1 ∩ E2) = `10/100`
∴ `"P"("E"_1/"E"_2) = ("P"("E"_1 ∩ "E"_2))/("P"("E"_2))`
= `(10/100)/(25/100)`
= `2/5`
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