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`

Answer 1

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`