If X B(35, p) such that 7 P(X=0)=P(X=1) then the value of P ( X =15) P ( X =20) is equal to

Step-by-step solution

Given that X B(35, p) with the condition 7P(X=0) = P(X=1) , we determine p from the binomial probability mass function: 7(1-p)³⁵ = 35p(1-p)³⁴ Dividing both sides by (1-p)³⁴ (since 0 7(1-p) = 35p 7 - 7p = 35p 7 = 42p p = 1 6 For the ratio P(X=15) P(X=20) , substitute p = 1 6 : P(X=15) P(X=20) = 35 15 ( 1 6 )¹⁵ ( 5 6 )²⁰ 35 20 ( 1 6 )²⁰ ( 5 6 )¹⁵ Using the identity 35 15 = 35 20 , the binomial coefficients cancel: P(X=15) P(X=20) = ( 1 6 )¹⁵ ( 5 6 )²⁰ ( 1 6 )²⁰ ( 5 6 )¹⁵ = ( 1 6 )⁻⁵ ( 5 6 )⁵ = 6^5 ( 5 6 )^5 = 5^5 5^5