Question

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 \(\frac{\mathrm{m}}{\mathrm{n}},\) where \(\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1,\) then \(\mathrm{m}+\mathrm{n}\) is equal to :

(1) 14

(2) 4

(3) 11

(4) 13
 

Answer 1

Correct option is (1) 14  

\(P=\frac{\frac{6}{10} \times \frac{5}{9}}{\frac{4}{10} \times \frac{6}{9}+\frac{6}{10} \times \frac{5}{9}}=\frac{5}{9}\)

\(\mathrm{m}=5, \mathrm{n}=9\)

\(\mathrm{m}+\mathrm{n}=14\)