WBJEE · Maths · Probability
The mean and variance of a binomial distribution are 4 and 2 respectively. Then the probability of exactly two succsses is
- A \(\frac{7}{64}\)
- B \(\frac{21}{128}\)
- C \(\frac{7}{32}\)
- D \(\frac{9}{32}\)
Answer & Solution
Correct Answer
(A) \(\frac{7}{64}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{np}=4, \mathrm{npq}=2\) \(\therefore \mathrm{q}=\frac{2}{4}=\frac{1}{2} \Rightarrow \mathrm{p}=\frac{1}{2} \therefore \mathrm{n}=8\) \(\mathrm{p}(\mathrm{x}=2)={ }^{8} \mathrm{C}_{2}\left(\frac{1}{2}\right)^{8}=\frac{28}{256}=\frac{7}{64}\)
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