Statistics And Probability Question 523
Question: The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is
[AIEEE 2004]
Options:
A) $ \frac{28}{256} $
B) $ \frac{219}{256} $
C) $ \frac{128}{256} $
D) $ \frac{37}{256} $
Show Answer
Answer:
Correct Answer: A
Solution:
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$ . \begin{matrix} np=4 \\\ npq=2 \\\ \end{matrix} \}\Rightarrow q=\frac{1}{2},\,p=\frac{1}{2},\,p=\frac{1}{2},n=8 $ $ P(X=2)={{\,}^{8}}C_2{{( \frac{1}{2} )}^{2}}{{( \frac{1}{2} )}^{6}}=28.\frac{1}{2^{8}}=\frac{28}{256} $ .
BETA
