Question

The probability that a student Ashu pass mathematics is 2/3,
The probability that he passed statistics is 4/9. If the probability of passing at least one subject is 4/5, what is the probability that Ashu will pass both the subjects.

Answer 1

Let $A=$ the event "a student Ashu pass mathematics".

Let $B=$ the event "a student Ashu pass a statistics".

Given that

$$P(A)={2\over 3},P(B)={4 \over 9},P(A\cup B)={4 \over 5}$$

Then

$$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$

$$P(A\cap B)=P(A)+P(B)-P(A\cup B)$$

$$P(A\cap B)={2\over 3}+{4\over 9}-{4\over 5}={14\over 45}$$

The probability that Ashu will pass both the subjects will be $14/45.$