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There are $a$ white and $b$ black balls in an Urn. A ball is drawn and its color is noted then the ball is replaced. If a second ball is drawn, the probability that both are white

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$\frac{a (a-1)}{{(a+b)}^{2}}$

$\frac{a^{2}}{{(a+b)}^{2}}$

$\frac{a (a - 1)}{(a+b) (a+b-1)}$

$\frac{a}{b}$

answer is B.

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Detailed Solution

$P (E_{1} \cap E_{2}) = P (E_{1}) . P (E_{2}) = (\frac{a}{a + b}) (\frac{a}{a + b}) = \frac{a^{2}}{{(a + b)}^{2}}$

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