Question

Let the random variables X follow B(6,p) If 16P(X=4)=P(X=2), then what is the value of p:

• A. (A) 13
• B. (B) 14
• C. (C) 15
• D. (D) 16

Answer 1

Answer: (C)

(C) 15

Answer 2

Explanation:
Binomial distribution: If a random variable X has binomial distribution as B (n, p) with n and p as parameters, then the probability of random variable is given as:P(X=k)=(nk)pk(1−p)n−kWhere, n is number of observations, p is the probability of success.Formula:Calculate combination:(nk)=n!(n−k)!k!Factorial:n!=1×2×3×…×(n−1)×nGiven: 16P(X=4)=P(X=2)
To find the value of p
Calculating probabilities of random variable X,
P(X=4)=(64)p4(1−p)2P(X=2)=(62)p2(1−p)4
Given,
16P(X=4)=P(X=2)⇒16(64)p4(1−p)2=(62)p2(1−p)4⇒16×6!2!4!p4(1−p)2=6!2!4!p2(1−p)4⇒16p2=(1−p)2⇒±4p=1−p⇒p=15 or p=−13So, p=15.Hence, the correct option is (C).