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BITSAT 2014
Exam
BITSAT
Year
2014
Subject
Mathematics
Chapter
Probability

BITSAT 2014 · Mathematics · Probability

A bag contains 5 brown and 4 white socks. A man pulls out 2 socks....

A bag contains 5 brown and 4 white socks. AA man pulls out 2 socks. Find the probability that they are of the same colour.

Options

  1. A49\frac{4}{9}
  2. B29\frac{2}{9}
  3. C59\frac{5}{9}
  4. D79\frac{7}{9}

Correct answer

A. 49\frac{4}{9}

Step-by-step solution

Let A \equivevent of twosocksbeingbrown.B≡two socks being brown. \mathrm{B} \equiv event of two socks being white.  Then \text{ Then }P(A)=(52)(92)=5.49.8=518,P(B) and =4C29C2=4.39.8=318\begin{aligned}& P(A)=\frac{\binom{5}{2}}{\binom{9}{2}}=\frac{5.4}{9.8}=\frac{5}{18}, \mathrm{P}(\mathrm{B})\\ \text{ and } =\frac{{ }^{4} \mathrm{C}_{2}}{{ }^{9} \mathrm{C}_{2}}=\frac{4.3}{9.8}=\frac{3}{18} \end{aligned}$Now,sinceNow, since\mathrm{A}andand\mathrm{B}aremutuallyexclusiveevents,sorequiredprobability=are mutually exclusive events, so required probability =\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})=\frac{5}{18}+\frac{3}{18}=\frac{4}{9}$
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