Question

A and B are two candidates seeking admission in I.I.T. The probability that A is selected is 0.5 and the probability that both A and B are selected is at most 0.3. Is it posssible that the probability of B getting selected is 0.9?

Answer 1

Let $A$ denote the event that the candidate A is selected and B the event that B is selected.
It is given that $P\left(A\right)=0.5$ ...(1)
$P(A\cap B)\le =0.3$ ...(2)

Now $P\left(A\right)+P\left(B\right)-P(A\cap B)=P(A\cup B)\le 1$
$\Rightarrow 0.5+P\left(B\right)-P(A\cap B)\le 1,$ by 1
$\Rightarrow P\left(B\right)\le 0.5+P(A\cap B)\le 0.5+0.3,$ by 2
$\Rightarrow P\left(B\right)\le 0.8$

Hence, $P\left(B\right)=0.9$ is not possible.