Probability Question 98
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:
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} $ .
BETA
