Statistics And Probability Question 504
Question: A bag contains 2 white and 4 black balls. A ball is drawn 5 times with replacement. The probability that at least 4 of the balls drawn are white is
[AMU 2001]
Options:
A) $ \frac{8}{141} $
B) $ \frac{10}{243} $
C) $ \frac{11}{243} $
D) $ \frac{8}{41} $
Show Answer
Answer:
Correct Answer: C
Solution:
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Probability for white ball $ =\frac{2}{6}=\frac{1}{3} $ Probability for black ball $ =\frac{4}{6}=\frac{2}{3} $
$ \therefore $ Required probability $ ={{,}^{5}}C_5{{( \frac{1}{3} )}^{5}},{{( \frac{2}{3} )}^{0}},+{{,}^{5}}C_4{{( \frac{1}{3} )}^{4}}( \frac{2}{3} ) $ $ ={{( \frac{1}{3} )}^{4}},[ \frac{1}{3}+5.,\frac{2}{3} ] $ $ =\frac{11}{3^{5}}=\frac{11}{243} $ .
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