Chance of an event happening is square of chance of a second event but odds against first are cube o

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14.Probability

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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 second. The chances of the events are

A

$\frac{1}{9},\,\frac{1}{3}$

B

$\frac{1}{{16}},\,\frac{1}{4}$

C

$\frac{1}{4},\,\frac{1}{2}$

D

None of these

Solution

(a) Let ${p_1},\,\,{p_2}$ be the chances of happenig of the first and second event respectively, then according to the given conditions, we have

${p_1} = p_2^2$ and $\frac{{1 – {p_1}}}{{{p_1}}} = {\left( {\frac{{1 – {p_2}}}{{{p_2}}}} \right)^3}$

$ \Rightarrow {p_2} = \frac{1}{3}$ and so ${p_1} = \frac{1}{9}.$

Standard 11

Mathematics

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