Statistics And Probability Question 286
Question: A drawer contains 5 brown socks and 4 blue socks well mixed. A man reaches the drawer and pulls out 2 socks at random. What is the probability that they match
Options:
A) $ \frac{4}{9} $
B) $ \frac{5}{8} $
C) $ \frac{5}{9} $
D) $ \frac{7}{12} $
Show Answer
Answer:
Correct Answer: A
Solution:
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Out of 9 socks, 2 can be drawn in $ {}^{9}C_2 $ ways. Two socks drawn from the drawer will match if either both are brown of both are blue. Therefore favourable number of cases is $ {}^{5}C_2+{}^{4}C_2. $ Hence the required probability $ =\frac{{}^{5}C_2+{}^{4}C_2}{{}^{9}C_2}=\frac{4}{9}. $
BETA
