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Question

A has 3 shares in a lottery containing 3 prizes and 9 blanks. B has two shares in a lottery containing 2 prizes and 6 blanks;compare their chance of success.

A
715:952
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B
952:715
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C
237:715
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D
952:237
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Solution

The correct option is A 952:715
Since A has three shares in a lottery, his change of success means that he gets at least one prize, that is,he gets either one prize or 2 prizes or 3 prizes 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=1q
We now find q.n=total no.of ways =12C3=12×11×101×2×3=220
Since out of 12 tickets in the lottery,he can draw any three tickets by virtue of his having three shares in the lottery and. m= favourable number of ways
=9C3=9×8×71×2×3=84,
Since he will fail to draw a prize if all the tickets drawn by him are blanks.q=mn=84220=2155.
p=As chance of success =12155=3455.
Similarly B's Chance of success p=1q=16C28C2=16×58×7=11528=1328.
As chance of success ; Bs chance of success =p;p=3455:1328=9521540:7151540=952:715.

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