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A and B are two horses. The probability of A winning a race is $\large\frac{1}{3}$ and that of horse B winning the same race, is $\large\frac{1}{5}$. The probability that none of them will win is :

$\begin {array} {1 1} (1)\;\large\frac{7}{15} & \quad (2)\;\large\frac{8}{15} \\ (3)\;\large\frac{1}{3} & \quad (4)\;None \: of \: these \end {array}$

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Using addition theorem of probability,
P ( A or B will win the race ) = $\large\frac{1}{3} + \large\frac{1}{5}$
$= \large\frac{8}{15}$
Hence P ( none of them will win the race ) = $1 - \large\frac{8}{15}$
$\large\frac{15-8}{15}$
$= \large\frac{7}{15}$
Ans : (1)
answered Jan 2, 2014

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