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Question

# The chance of an events happening is the square of the chance of the a second events but the odds against the fist are the cube of the odds against the second . Then , the of the first events happening is

A
19
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B
13
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C
12
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D
18
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Solution

## The correct option is A 19Let the chance of second event be p∴ The chance of first event be p2.Now odds against the first event =q1p1=1−p2p2odds against the second event =q2p2=1−ppSince the odds against the first are the cubes of the odds against the second therefore1−p2p2=(1−pp)3⇒(1−p)(1+p)p2=(1−p)3p3⇒p(1+p)=(1−p)2⇒p2+p=p2−2p+1Therefore the chance of the first event is p2=19

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