Question

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

विकल्प

• 1320

• 1088

• `120/1331`

• `1088/1089`

Answer 1

If a random variable X follows the Binomial distribution B (33, p) such that 3P(X = 0) = P(X = 1), then the value of `(P(X = 15))/(P(X = 18)) - (P(X = 16))/(P(X = 17))` is equal to 1320.

Explanation:

Let the probability of success is p and q = 1 – p.

Here, n = 33

3P(x = 0) = P(x = 1)

3. ³³C₀ (q)³³ = ³³C₁ pq³²

p = `1/12`, q = `11/12`, `q/p` = 11  ...(i)

`(P(X = 15))/(P(X = 18)) - (P(X = 16))/(P(X = 17))`

`(""^33C_15  p^15  q^18)/(""^33C_18  p^18  q^15) - (""^33C_16  p^16  q^17)/(""^33C_17  p^17  q^16) = (q/p)^3 - (q/p)`

= (11)³ – 11  ...[From (i)]

= 1320