Question

For the binomial distribution X ∼ B(n, p), n = 6 and P(X = 4) = P(X = 2). find p.

Answer 1

P(X = 4) = ⁶C₄p⁴q₂ and

P(X = 2) = ⁶C₂p²q⁴

But P(X = 4) = P(X = 2)  ...(Given)

∴ ⁶C₄p⁴q² = ⁶C₂p²q⁴

Now ⁶C₄ = ⁶C₂

∴ ⁶C₂p⁴q² = ⁶C₂p²q²

∴ p⁴q² = p²q²

∴ p² = q²

Also q = 1 – p

∴ q² = (1 – p)²   ...(Squaring)

∴ p² = 1 – 2p + p²   ...(∵ p² = q²)

∴ 2p = 1,

∴ p = `1/2`