If a random variable X follows the Binomial distribution B 33 , p such that 3 P X = 0 = P X = 1 , then the value of P X = 15 P X = 18 - P X = 16 P X = 17 is equal to

Step-by-step solution

We know that p = success, q = failure Given 3 P X = 0 = P X = 1 3 C 0 33 p 0 q 33 = C 1 33 p 1 q 32 3 × 1 × q = 33 × p q = 11 p       . . .   i Also p + q = 1 Now from equation i ,   p + 11 p = 1 12 p = 1 p = 1 12 ,   q = 11 12 Now P X = 15 P X = 18 - P X = 16 P X = 17 ⇒ C 15 33 p 15 q 18 C 18 33 p 18 q 15 - C 16 33 p 16 q 17 C 17 33 p 17 q 16 = q 3 p 3 - q p = q p q p 2 - 1 = 11 1 11 2 - 1 = 11 × 120 = 1320