Quantitative Aptitude Ques 1594

Question: Three numbers are chosen from 1 to 8. Find the probability for the 3 chosen numbers to be consecutive.

Options:

A) $ \frac{11}{28} $

B) $ \frac{3}{28} $

C) $ \frac{5}{28} $

D) $ \frac{9}{28} $

Show Answer

Answer:

Correct Answer: B

Solution:

  • The total number of ways of choosing 3 number out of $ 8={}^{8}C _3 $ way Let E be the event of the three numbers to b consecutive $ E={(1,2,3), $ $ (2,3,4), $ $ (3,4,5), $ $ (4,5,6), $ $ (5,6,7), $ $ (6,7,8)} $

$ \therefore $ $ P(E)=\frac{n(E)}{n(S)}=\frac{6}{{}^{8}C _3}=\frac{6}{56}=\frac{3}{28} $

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