# Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X. - Mathematics and Statistics

Sum

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

#### Solution

Let X denote the number of sixes.

∴ Possible values of X are 0, 1, 2.

Let P(getting six when a die is thrown) = p = (1)/(6)

∴ q = 1 – p = 1 - (1)/(6) = (5)/(6)

∴ P(X = 0) = P(no six) = qq = q2 = (5/6)^2 = (25)/(36)

P(X = 1) = P(one six) = pq + qp = 2pq

= 2(1/6)(5/6)

= (10)/(36)

P(X = 2) = P(two sixes) = pp = p2 = (1/6)^2 = (1)/(36)
Expectation of X
= E(X)

= $\sum\limits_{i=1}^{3} x_i.\text{P}(x_i)$

= 0 xx (25)/(36) + 1 xx (10)/(36) + 2 xx (1)/(36)

= (1)/(36)(0 + 10 + 2)

= (1)/(3).

Concept: Mean of a Random Variable
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Probability Distributions
Exercise 8.1 | Q 1.12 | Page 141