MHT CET · Maths · Probability
The probability of success for the Binomial distribution satisfying the relation, \(4 P(X=4)=P(X=2)\) and having the parameter \(n=6\), is
- A \(\frac{1}{5}\)
- B \(\frac{5}{6}\)
- C \(\frac{1}{6}\)
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{3}\)
Step-by-step Solution
Detailed explanation
\(4 \cdot P(x=4)=P(x=2) \)
\( \Rightarrow 4 \cdot{ }^6 C_4 P^4 \cdot q^2={ }^6 C_2 p^2 q^4 \)
\( \Rightarrow \frac{p^2}{q^2}=\frac{1}{4}\)
\(\Rightarrow 3 p=1 \)
\( \Rightarrow p=\frac{1}{3}\)
\( \Rightarrow 4 \cdot{ }^6 C_4 P^4 \cdot q^2={ }^6 C_2 p^2 q^4 \)
\( \Rightarrow \frac{p^2}{q^2}=\frac{1}{4}\)
\(\Rightarrow 3 p=1 \)
\( \Rightarrow p=\frac{1}{3}\)
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