A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is

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$\frac{5}{6}$

$\frac{5}{7}$

$\frac{3}{7}$

$\frac{2}{7}$

answer is B.

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Detailed Solution

Required probability
$\begin{array}{l} \frac{^{5} C_{2} +^{6} C_{2}}{^{2} C_{2} +^{3} C_{2} +^{4} C_{2} +^{5} C_{2} +^{8} C_{2}} \\ = \frac{10 + 15}{1 + 3 + 6 + 10 + 15} = \frac{25}{35} = \frac{5}{7} \end{array}$

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