Quantitative Aptitude Ques 2383

Question: 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?

Options:

A) $ \frac{5}{33} $

B) $ \frac{5}{22} $

C) $ \frac{7}{22} $

D) $ \frac{7}{33} $

E) $ \frac{7}{66} $

Show Answer

Answer:

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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