Two balls are selected at random one by one without replacement f… - Vidyadip

MCQ

Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball is black, given that the second selected ball is also black, is $\frac{ m }{ n }$, where $\operatorname{gcd}( m , n )=1$, then $m + n$ is equal to :

✓
14
B
4
C
11
D
13

✓

Answer

Correct option: A.

14

(A) 14
$
\begin{array}{l}
Sol.P=\frac{\frac{6}{10} \times \frac{5}{9}}{\frac{4}{10} \times \frac{6}{9}+\frac{6}{10} \times \frac{5}{9}}=\frac{5}{9} \\
m=5, n=9 \\
m+n=14
\end{array}
$

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