In a Binomial distribution B(n,p), n=6 and 9P(X=4)=P(X=2). What is p equal to?
- A. \frac{1}{4} ✓
- B. \frac{1}{2}
- C. \frac{3}{4}
- D. \frac{4}{5}
Correct Answer: A. \frac{1}{4}
Explanation
From the binomial probability formula, P(X=r) = {}^nC_r p^r q^{n-r}. We are given 9 \times {}^6C_4 p^4 q^2 = {}^6C_2 p^2 q^4. Since {}^6C_4 = {}^6C_2 = 15, this simplifies to 9p^2 = q^2. Taking the positive square root gives 3p = q. Since p+q = 1, we substitute q to get 3p = 1-p \implies 4p = 1 \implies p = \frac{1}{4}.
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