Question

A and B are two candidates for seeking admission in IIT. The probability that A is selected is 0.4 and the probability that both A and B are selected is at the most 0.2. Then P(B) is less than:

• A. 0.9
• B. 0.7
• C. 0.8
• D. None

Answer 1

The correct option is C 0.8

$\text{Given:}P\left(A\right)=0.4,P(A\cap B)\le \mathrm{0.2.}P(A\cup B)\le 1\Rightarrow P\left(A\right)+P\left(B\right)-P(A\cap B)\le 1\Rightarrow P\left(B\right)\le 1-0.4+P(A\cap B)\le 0.6+0.2=\mathrm{0.8.}$