Question

# A has 3 tickets of a lottery containing 3 prizes and 9 blanks. B has two tickets of another lottery containing 2 prizes and 6 blanks. The ratio of their chances of success is

A
3255:1528
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B
3255:1328
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C
3455:1328
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D
3455:1528
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Solution

## The correct option is A 3455:1328Since A has 3 shares in a lottery, his chance of success means that he gets at least 1 prize or 2 prize or 3 prize and his chance of failure means that he gets no prize. It is certain that either he succeeds or fails.If p denotes his chance of success and q the chance of his failure then, p+q=1 or p=1−qWe know q×n= total number of ways=12C1=12×11×101×2×3=220Since out of 12 tickets in the lottery, he can draw any 3 tickets by virtue of his having 3 shares in the lottery and m= favourable number of ways =9C3=9×8×71×2×3=84Since he will fail to draw a prize if all the tickets draw by him are blanks.∴q=mn=84220=2155∴p= A′s chance of success =1−2155=3455Similarly, B′s chance of successp′=1−q′=1−6C28C2=1−6×58×7=1−1528=1328∴ A′s chance of success=B′s chance of success.=P:P′=3435:1328

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