Quantitative Aptitude Ques 558
Question: A bag contains 5 red balls, 6 yellow balls and 3 green balls. If two balls are picked at random, what is the probability that either both are red or both are green in colour? [SBI (PO) 2016]
Options:
A) $ \frac{3}{7} $
B) $ \frac{5}{14} $
C) $ \frac{1}{7} $
D) $ \frac{2}{7} $
E) $ \frac{3}{14} $
Show Answer
Answer:
Correct Answer: C
Solution:
- Probability of 2 red balls $ =\frac{{}^{5}C _2}{{}^{14}C _2} $ Probability of 2 green balls $ =\frac{{}^{3}C _2}{{}^{14}C _2} $
$ \therefore $ Required probability $ =\frac{{}^{5}C _2}{{}^{14}C _2}+\frac{{}^{3}C _2}{{}^{14}C _2} $ $ =\frac{\frac{5\times 4}{1\times 2}}{\frac{14\times 13}{1\times 2}}+\frac{\frac{3,\times 2}{1\times 2}}{\frac{14\times 13}{1\times 2}} $ $ =\frac{20+6}{14\times 13}=\frac{2}{14}=\frac{1}{7} $
BETA
