Quantitative Aptitude Ques 1243

Question: A number is chosen at random among the first 100 natural numbers. Find the probability of the number chosen to be a multiple of 7.

Options:

A) $ \frac{3}{50} $

B) $ \frac{7}{50} $

C) $ \frac{11}{50} $

D) $ \frac{9}{50} $

Show Answer

Answer:

Correct Answer: B

Solution:

  • Total number of ways of selecting one number from 100 numbers is $ {}^{100}C _1, $ ways. Let E be the event of drawing a multiple of 7. Then, $ E={7, $ $ 14, $ $ 21, $ $ 28, $ $ 35, $ $ 42, $ $ 49, $ $ 56, $ $ 63, $ $ 70, $ $ 77, $ $ 84, $ $ 91, $ $ 98} $

$ \therefore $ $ P(E)=\frac{n(E)}{n(S)}=\frac{14}{{}^{100}C _1}=\frac{14}{100}=\frac{7}{50} $

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