Question

In three throws with a pair of dice find the chance of throwing doublets at least twice.

Answer 1

For a pair of dice, out of 36 sample points there are 6 doublets, namely

(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)

∴ p = `6/36 = 1/6`,

∴ q = `1 - 1/6 = 5/6`

and n = 3

∴ P(at least 2 success)

= P(X = 2) + P(X = 3)

= `""^3C_2 (1/6)^2(5/6) + ""^3C_3 (1/6)^3(5/6)^0`

= `3(5/216) + 1/216`

= `16/216`

= `2/27`