| 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] |
A) \[\frac{3}{7}\]
B) \[\frac{5}{14}\]
C) \[\frac{1}{7}\]
D) \[\frac{2}{7}\]
E) \[\frac{3}{14}\]
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 \[=\frac{{}^{5}{{C}_{2}}}{{}^{14}{{C}_{2}}}+\frac{{}^{3}{{C}_{2}}}{{}^{14}{{C}_{2}}}\] |
| \[=\frac{\frac{5\times 4}{1\times 2}}{\frac{14\times 13}{1\times 2}}+\frac{\frac{3\,\times 2}{1\times 2}}{\frac{14\times 13}{1\times 2}}\] |
| \[=\frac{20+6}{14\times 13}=\frac{2}{14}=\frac{1}{7}\] |
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