Question

If X ~ B(6, p) and 2·P(X = 3) = P(X = 2), then find p.

Answer 1

P(X = x) = ⁿC_xp^xq^{n – x}, where n = 6

∴ P(X = x) = ⁶C_xp^xq^{6 – x}

Given: 2·P(X = 3) = P(X = 2)

∴ 2 × ⁶C₃p³q^{6 – 3} = ⁶C₂p²q^{6 – 2}

∴ `2 xx (6 xx 5 xx 4)/(1 xx 2 xx 3)*p^3q^3 = (6 xx 5)/(1 xx 2)p^2q^4`

∴ 40p = 15q = 15(1 – p)

∴ 40p = 15 – 15p

∴ 55p = 15

∴ p = `15/55 = 3/11`