Question

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

• A. $\frac{4}{9}$
• B. $\frac{2}{9}$
• C. $\frac{5}{9}$
• D. $\frac{7}{9}$

Answer 1

Answer: (A)

Total number of socks $=9(4 B , 5 W )$
Required probability $= P ( B , B )$ orP $( W , W )$
$= P ( B ) P ( B )+ P ( W ) P ( W )$
Probability of pulling a brown socks in first draw is $\frac{4}{9}$
Since, the socks is not replaced, probability of pulling a brown socks in second draw is $\frac{3}{8}$
Probability of pulling a white socks in first draw is $\frac{5}{9}$
Since, the socks is not replaced, probability of pulling a white socks in second draw is $\frac{4}{8}$
Required probability $=\frac{4}{9} \times \frac{3}{8}+\frac{5}{9} \times \frac{4}{8}$
$=\frac{3}{18}+\frac{5}{18}=\frac{4}{9}$