| A bag contains 7 blue balls and 5 yellow balls. If two balls are selected at random, then what is the probability that none is yellow? |
A) \[\frac{5}{33}\]
B) \[\frac{5}{22}\]
C) \[\frac{7}{22}\]
D) \[\frac{7}{33}\]
E) \[\frac{7}{66}\]
Correct Answer: C
Solution :
| Total balls in the bag = 7 blue\[+5\] yellow = 12 balls |
| Number of ways to choose 2 balls out of 12 \[={}^{12}{{C}_{2}}\] |
| \[=\frac{12!}{2!10!}=\frac{12\times 11}{1\times 2}=66\] |
| P (no ball is yellow) = P (both balls are blue) |
| Number of selecting 2 blue balls |
| \[={}^{7}{{C}_{2}}=\frac{7!}{2!5!}=\frac{7\times 6}{1\times 2}=21\] |
| \[\therefore \] Required probability \[=\frac{21}{66}=\frac{7}{22}\] |
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