Q14 of 54 Page 314

The probability that a new car will get aaward for its design is 0.25, the probability that it will get an award for efficient use of fuel is 0.35 and the probability that it will get both the awards is 0.15. Find the probability that

(i) it will get atleast one of the two awards


(ii) it will get only one of the awards.

Let the probability of winning the award for design be P(A) and that for efficient use of fuel be P(B)


P(A) = 0.25


P(B) = 0.35


P(A ∩B) = 0.15


(i) probability that it will get at least one of the two awards


P(AUB) = P(A)+P(B)- P(A ∩B)


= 0.25+0.35-0.15


= 0.45


(ii) probability of getting only oner = P(A)+P(B)-2. P(A ∩B)


= 0.25+0.35-2(0.15)


= 0.3


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