Question

If a random variable X follows the Binomial distribution B(5, p) such that P(X = 0) = P(X = 1), then `(P(X = 2))/(P(X = 3))` is equal to ______.

Options

• 1

• 10

• 25

• 5

Answer 1

If a random variable X follows the Binomial distribution B(5, p) such that P(X = 0) = P(X = 1), then `(P(X = 2))/(P(X = 3))` is equal to 5.

Explanation:

Given B(5, P) and P(X = 0) = P(X = 1)

ⁿc₀xⁿy⁰ = nC₁x^n–1y

`(underline(|x))/(underline(|0)  underline(|x - 0)) x^n = (underline(|x))/(underline(|1)  underline(|x - 1)) x^n/x y` `\implies x/y` = n  ...(i)

Now, `(P(X = 2))/(P(X = 3)) = (""^nC_2x^(n - 2)y^2)/(""^nC_3x^(n - 3)y^3) = (""^5C_2)/(""^5C_3).x/y`

= 1. n = n   ...(From (i))

Therefore, n = 5