Question

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

Answer 1

Answer is "14"  

\(P\left(\frac{1 \text { st is as so black }}{2 \text { nd is black }}\right)\)   

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

\(=\frac{30}{24+30}=\frac{30}{54}=\frac{5}{9}\)  

\(\mathrm{m}+\mathrm{n}=5+9=14\)