Quantitative Aptitude Ques 1535

Question: Out of 30 consecutive positive integers, two are chosen at random. Find the probability of their sum to be even.

Options:

A) $ \frac{14}{29} $

B) $ \frac{11}{29} $

C) $ \frac{17}{29} $

D) $ \frac{19}{29} $

Show Answer

Answer:

Correct Answer: A

Solution:

  • (a) The total number of ways of choosing two out of 30, i.e. $ {}^{30}C _2 $ ways. Let E = Event of choosing two numbers such that their sum is even.
    $ \therefore $ $ P(E)=\frac{n(E)}{n(S)}=\frac{{}^{15}C _2+{}^{15}C _2}{{}^{30}C _{12}} $ $ =\frac{105+105}{435}=\frac{210}{435}=\frac{14}{29} $
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