Probability Question 2
Question: In from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be drawn is
Options:
A) $ \frac{13}{32} $
B) $ \frac{1}{4} $
C) $ \frac{1}{32} $
D) $ \frac{3}{16} $
Show Answer
Answer:
Correct Answer: A
Solution:
P (2 white and 1 black)
$ =P(W_1W_2B_3orW_1B_2W_3orB_1W_2W_3) $
$ =P(W_1W_2B_3)+P(W_1B_2W_3)+P(B_1W_2W_3) $
$ =P(W_1)P(W_2)P(B_3)+P(W_1)P(B_2)P(W_3)+ $ $ P(W_1)(W_2)(W_3) $
$ =\frac{3}{4}.\frac{2}{4}.\frac{3}{4}+\frac{3}{4}.\frac{2}{4}.\frac{1}{4}+\frac{1}{4}.\frac{2}{4}.\frac{1}{4}=\frac{1}{32}(9+3+1)=\frac{13}{32} $
BETA
