Question

A fair die thrown once. A person will gets Rs. 5 if the faces of a die results in mulitple of 2. other wise he loses Rs. 2. find his expected amount.

Answer 1

Let x denote the expected amount is random variable which can take: 5 (die results in multiple of 2 : 2.46) and -2( die results in 1, 3, 5), with respective probabilities.

P(x = 5) = P(getting multiple of 2) = 3/6 = 1/2

P(x = -2) = P(Not getting multiple 2) = 3/6 = 1/2

The probability distribution is :

Expected amount: E(x) = Σx. P(x)