Question

A and B are two candidates seeking admission in IIT. The probability that A is selected is 0.5 and the probability that A selected is 0.6 and the probability that both A and B are selected is atmost 0.3. Is it possible that the probability of B getting selected is 0.9 ?

Answer 1

Given , `P(A) =0.5 and P(A cap B ) le 0.3`
`implies P(A) +P(B) -P(A cup B) le 0.3`
`implies P(B) le 0.3+ P(A cup B ) -P(A) le P(A cup B )-0.2 " " ["since, " P(A cup B) le 1 implies P(A cup B ) -0.2 le 0.8 ]`
`:. P(B) le 0.8`
`impliesP(B)` cannot be 0.9 .