Subject: General Aptitude · Chapter: Probability · Exam: · Marks: · Difficulty:
A bag contains 10 mangoes out of which 4 are taken out together. If one of them is found to be good, the probability that other is also good is [DMRC-Train Operator (Station Controller) Exam, 2016]
(a)$\frac{1}{3}$
(b)$\frac{8}{15}$
(c)$\frac{5}{18}$
(d)$\frac{2}{3}$
Answer
Answer (as printed): A
Explanation
Out of 10 mangoes, 4 mangoes are rotten $$\begin{aligned} \therefore \text { Required probability } & =\frac{{ }^{6} C_{2}}{{ }^{10} C_{2}}=\frac{\frac{6!}{2!(6-2)!}}{\frac{10!}{2!(10-2)!}}=\frac{\frac{6!}{2!4!}}{\frac{10!}{2 \times 8!}} \\ & =\frac{\frac{6 \times 5}{1 \times 2}}{\frac{10 \times 9}{1 \times 2}}=\frac{6 \times 5}{10 \times 9}=\frac{1}{3} \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.