Probability Question 299
Question: A box contains 20 identical balls of which 10 are blue and 10 are green. The balls are drawn at random from the box. One at a time with replacement. The probability that a blue ball is drawn 4th time on the 7th draw is
Options:
A) $ \frac{27}{32} $
B) $ \frac{5}{64} $
C) $ \frac{5}{32} $
D) $ \frac{1}{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
Probability of getting a blue ball at any draw $ =p=\frac{10}{20}=\frac{1}{2} $
P [getting a blue ball 4th time in 7th draw] =P [Getting 3 blue balls in 6 draws] $ \times P $ [A blue ball in the 7th draw].
$ {{=}^{6}}C_3{{( \frac{1}{2} )}^{3}}{{( \frac{1}{2} )}^{3}}.\frac{1}{2} $
$ =\frac{6\times 5\times 4}{1\times 2\times 3}{{( \frac{1}{2} )}^{7}}=20\times \frac{1}{32\times 4}=\frac{5}{32} $
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