Question:
If a random variable X follows the Binomial distribution B(5, p) such that P(X = 0) = P(X = 1), then \( {{P(X = 2)} \over {P(X = 3)}} \) is equal to :
If a random variable X follows the Binomial distribution B(5, p) such that P(X = 0) = P(X = 1), then \( {{P(X = 2)} \over {P(X = 3)}} \) is equal to :
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Use P(X=r) = C(5,r) p^r q^(5-r); equate P(0) and P(1) to get p, then take the ratio P(2)/P(3).
Updated On: Oct 31, 2026
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The Correct Option is D
Solution and Explanation
Step 1: \( P(X=0)=q^5 \), \( P(X=1)=5pq^4 \). Equal gives \( q=5p \).
Step 2: With \( p+q=1 \): \( 6p=1 \Rightarrow p=\frac16,\ q=\frac56 \).
Step 3: \( \frac{P(2)}{P(3)}=\frac{\binom52 p^2q^3}{\binom53 p^3q^2}=\frac{10\,p^2q^3}{10\,p^3q^2}=\frac{q}{p}=5 \).
Answer: (D) 5
Step 2: With \( p+q=1 \): \( 6p=1 \Rightarrow p=\frac16,\ q=\frac56 \).
Step 3: \( \frac{P(2)}{P(3)}=\frac{\binom52 p^2q^3}{\binom53 p^3q^2}=\frac{10\,p^2q^3}{10\,p^3q^2}=\frac{q}{p}=5 \).
Answer: (D) 5
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