Question

If X ∼ B(n, p), n = 6 and 9 P(X = 4) = P(X = 2), then find the value of p.

Answer 1

9 P(X = 4) = P(X = 2)   ...(Given)

9 · ⁶C₄ p⁴ q² = ⁶C₂ p² q⁴  ...(∵ n = 6)

But ⁶C₄ = ⁶C₂

∴ 9p⁴q² = p²q⁴

`(9p^4)/p^2 = q^4/q^2`

∴ 9p² = q²

∴ 9p² = (1 – p)²

∴ 9p² = 1 – 2p + p²

∴ 8p² + 2p – 1 = 0

∴ (4p – 1)(2p + 1) = 0

∴ p = `1/4` as p ≠ `-1/2`