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The chance of an event happening is the square of the chance of a second event but the odds against the first are the cube of the odds against the sec

Monjur Alahi

The chance of an event happening is the square of the chance of a second event but the odds against the first are the cube of the odds against the second. The chances of the events are
A. `P_(1) = 1//9`
B. `P_(1) = 1//16`
C. `P_(2) = 1//3`
D. `P_(2) = 1//4`


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Salim Ahmed Kawsar

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Correct Answer - A::C
Let `p_(1), p_(2)` be the chances of happening of the first and second events, respectively. Then according to the given conditions, we have
`p_(1) = p_(2)^(2)`
and `(1-p_(1))/(p_(1)) = ((1-p_(2))/(p_(2)))^(3)`
Hence,
`(1-p_(2)^(2))/(p_(2)^(2)) = ((1-p_(2))/(p_(2)))^(3) or p_(2)(1 + p_(2)) = (1 - p_(2))^(2)`
or `3p_(2) = 1 or p_(2) = (1)/(3) " and so "p_(1) = (1)/(9)`

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