JEE Mains · Maths · STD 12 - 13. probability
Let in a Binomial distribution, consisting of \(5\) independent trials, probabilities of exactly \(1\) and \(2\) successes be \(0.4096\) and \(0.2048\) respectively. Then the probability of getting exactly \(3\) successes is equal to ....... .
- A \(\frac{32}{625}\)
- B \(\frac{80}{243}\)
- C \(\frac{40}{243}\)
- D \(\frac{128}{625}\)
Answer & Solution
Correct Answer
(A) \(\frac{32}{625}\)
Step-by-step Solution
Detailed explanation
\(P ( X =1)={ }^{5} C _{1} \cdot p \cdot q ^{4}=0.4096\) \(P ( X =2)={ }^{5} C _{2} \cdot p ^{2} \cdot q ^{3}=0.2048\) \(\Rightarrow \frac{ q }{2 p }=2\) \(\Rightarrow q=4 p\) and \(p+q=1\) \(\Rightarrow p=\frac{1}{5}\) and \(q=\frac{4}{5}\) Now…
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