MHT CET · Maths · Probability
If \(x\) follows the Binomial distribution with parameters \(n=6\) and \(p\) and \(9 P(X=4)\) \(=P(X=2)\), then \(p\) is
- A \(1 / 4\)
- B \(1 / 3\)
- C \(1 / 2\)
- D \(2 / 3\)
Answer & Solution
Correct Answer
(A) \(1 / 4\)
Step-by-step Solution
Detailed explanation
Given, \(9 P(X=4)=P(X=2)\)
\(\therefore \quad 9 \cdot{ }^{6} C_{4} p^{4}(1-p)^{2}={ }^{6} C_{2} p^{2}(1-p)^{4}\)
\(\Rightarrow \quad \frac{(1-p)^{2}}{p^{2}}=9\)
\(\Rightarrow \quad \frac{1-p}{p}=3\)
\(\Rightarrow \quad p=1 / 4\)
\(\therefore \quad 9 \cdot{ }^{6} C_{4} p^{4}(1-p)^{2}={ }^{6} C_{2} p^{2}(1-p)^{4}\)
\(\Rightarrow \quad \frac{(1-p)^{2}}{p^{2}}=9\)
\(\Rightarrow \quad \frac{1-p}{p}=3\)
\(\Rightarrow \quad p=1 / 4\)
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