If A and B are two candidates seeking admission in an engineering College.

Question

State whether the statement are True or False.

If A and B are two candidates seeking admission in an engineering College. The probability that A is selected is .5 and the probability that both A and B are selected is at most .3. Is it possible that the probability of B getting selected is 0.7?

Answer 1

Let E₁ be the event that A is selected in engineering college

and E₂ be the event that B is selected in engineering college

Then, we have

P(E₁) = 0.5, P(E₂) = 0.7 and P(E₁⋂ E₂) ≤ 0.3

Now, P(E₁) × P(E₂) ≤ 0.3

⇒ 0.5 × P(E₂) ≤ 0.3

⇒ P(E₂) ≤ 0.6

But P(E₂) = 0.7

Hence, the given statement is False.