Probability Question 94
Question: A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that these are of the same colour is
[UPSEAT 1999; MP PET 2000]
Options:
A) $ \frac{5}{108} $
B) $ \frac{18}{108} $
C) $ \frac{30}{108} $
D) $ \frac{48}{108} $
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Answer:
Correct Answer: D
Solution:
Total socks $ =5+4=9 $
The number of ways to select $ 2 $ socks out of 9 = $ ^{9}C_2 $
If number of ways to select both brown socks $ ={{}^{5}}C_2 $
And number of ways to select both white socks $ ={{}^{4}}C_2 $
$ \therefore P $ (Both brown or white) $ =\frac{^{5}C_2+{{}^{4}}C_2}{^{9}C_2}=\frac{16}{36}=\frac{48}{108} $ .
BETA
