Quantitative Aptitude Ques 2450

Question: A bag contains 5 white and 3 black balls and 4 balls are successively drawn out and not replaced. The probability that they are alternately of different colours, is

Options:

A) $ \frac{1}{196} $

B) $ \frac{2}{7} $

C) $ \frac{13}{56} $

D) $ \frac{1}{7} $

Show Answer

Answer:

Correct Answer: D

Solution:

  • Required probability =P(WBWB) + P(BWBW) $ =( \frac{{}^{3}C _1\times {}^{5}C _1\times {}^{2}C _1\times {}^{4}C _1}{{}^{8}C _1\times {}^{7}C _1\times {}^{6}C _1\times {}^{5}C _1} )+( \frac{{}^{3}C _1\times {}^{5}C _1\times {}^{2}C _1\times {}^{4}C _1}{{}^{8}C _1\times {}^{7}C _1\times {}^{6}C _1\times {}^{5}C _1} ) $ $ =\frac{1}{14}+\frac{1}{14}=\frac{2}{14}=\frac{1}{7} $
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