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Solution :

Given , `P(A) =0.5 and P(A cap B ) le 0.3` <br> `implies P(A) +P(B) -P(A cup B) le 0.3` <br> `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 ]` <br> `:. P(B) le 0.8` <br> `impliesP(B)` cannot be 0.9 .