A box contains 6 red and 4 blue marbles Two marbles are with

A box contains 6 red and 4 blue marbles. Two marbles are withdrawn randomly. If they are the same color you win $1.10, if they are different colors you lose $1.00.

What is the expected amount you win (or lose)?

Solution

Let Ri denote the event, “red on ith draw.” Then, P(R1 R2) = (6/10)(5/9)
and P(R1\' R2\')= (6/10)(5/9) , Let X denote the win, where X < 0 means loss.
Then, P{X = 1.10} = 2×(6/10)(5/9) = 2/3, and P{X = 1} = 5/9.

You win the trials = 2/3
Therefore,You loose the money {{X=-1} =1/3

Expected Mean = 1.1*2/3 - 1/3= 2/5 = 0.4