Question

A game consists of flipping a fair coin twice and counting the number of heads that appear. The distribution for the number of heads, X, is given by: P(X = 0) = 1/4; P(X =1) = 1/2; P(X = 2) = 1/4. A player receives $0 for no heads, $2 for 1 head, and $5 for 2 heads (there is no cost to play the game). Calculate the expected amount of winnings ($).

Answer 1

Given that, counting the number of heads that appear. The distribution for the number of heads, X, is given by: P(X = 0) = 1/4; P(X =1) = 1/2; P(X = 2) = 1/4

A player receives $0 for no heads, $2 for 1 head, and $5 for 2 heads (there is no cost to play the game).

The expected amount of winning is,

= [0 × P(x = 0)] + [ 2 × P(x = 1)] + [ 5 × P(x = 2) ]

= [ 0 × 1/4] + [ 2 × 1/2 ] + [ 5 × 1/4 ]

= 0 + 1 + 1.25

= 2.25

Therefore, the expected amount of winnings is $ 2.25