Question

Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.

Answer 1

Here, X represents the number of sixes obtained when two dice are thrown simultaneously. Therefore, X can take the value of 0, 1, or 2.

∴ P (X = 0) = P (not getting six on any of the dice)

= `(5 xx 5)/(6 xx 6)`

= `25/36`

P (X = 1) = P (six on first die and no six on second die) + P (no six on first die and six on second die)

= `2(1/6xx5/6)`

= `10/36`

P (X = 2) = P (six on both the dice) =`1/36`

∴ The required probability distribution is as follows.

X	0	1	2
P(X)	`25/36`	`10/36`	`1/36`

Expectation of X = E(X) = `sum X_iP(X_i)`

= `0 xx 25/36 + 1 xx10/36 + 2xx 1/36`

= `1/3`