Question

In a certain school, 20% of the students failed in English, 15% of the students failed
in mathematics, and 10% of the students failed both English and mathematics. A
student is selected at random and found that he failed in English, what is the
probability that he also failed in Mathematics?

Answer 1

Required Probability = 0.5

Step-by-step explanation:

We are given that in a certain school, 20% of the students failed in English, 15% of the students failed  in mathematics, and 10% of the students failed in both English and mathematics.

Let Probability that students failed in English = P(E) = 0.20

Probability that students failed in mathematics = P(M) = 0.15

Probability that students failed in both English and mathematics = $P(E \bigcap M)$ = 0.10

Now, a student is selected at random and found that he failed in English,  probability that he also failed in Mathematics is given by = P(M/E)

The conditional probability of P(A/B) is given as;

                   P(A/B) = $\frac{P(A \bigcap B)}{P(B)}$

Similarly, P(M/E) = $\frac{P(M \bigcap E)}{P(E)}$    

                            = $\frac{0.10}{0.20}$            { $\because P(E \bigcap M) = P(M \bigcap E)$ }

                            = 0.5

Therefore, required conditional probability is 0.5 .