What is the value of k?
Consider the following for the two (02) items that follow :<br>Let X be a random variable following binomial distribution with parameters n=6 and p=k. Further, 9P(X=4)=P(X=2).
- A. 1/2
- B. 1/3
- C. 1/4 ✓
- D. 1/5
Correct Answer: C. 1/4
Explanation
Given 9 \binom{6}{4} k^4 (1-k)^2 = \binom{6}{2} k^2 (1-k)^4. Since \binom{6}{4} = \binom{6}{2}, this simplifies to 9k^2 = (1-k)^2. Taking the positive square root (k \gt 0), 3k = 1 - k \implies 4k = 1 \implies k = 1/4.
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