If a random variable X follows the Binomial distribution B(10, p) such that 5 P(X=0)=P(X=1) , then the value of P(X=5) P(X=6) is equal to

Step-by-step solution

Given X B(10, p) with the condition 5P(X=0) = P(X=1) . The probability P(X=0) = (1-p)¹⁰ and P(X=1) = 10p(1-p)^9 . Substituting into the given relation yields 5(1-p)¹⁰ = 10p(1-p)^9 . For p 1 , dividing both sides by (1-p)^9 gives 5(1-p) = 10p , leading to p = 1 3 . The ratio P(X=5) P(X-6) simplifies to 10 5 10 6 1-p p . Using the identity 10 5 10 6 = 6 5 and substituting p = 1 3 , 1-p = 2 3 , we obtain: P(X=5) P(X=6) = 6 5 2/3 1/3 = 6 5 2 = 12 5 . Final answer: 12 5