If Melinda buys 2 tickets to the raffle in exercise 19 what

If Melinda buys 2 tickets to the raffle in exercise 19, what is her expectation? (#19: Melinda buys (1) raffle ticket at the spring fling since there is (1) 1,000 prize, (1) $500 prize, and (5) $100 prizes. There were a total of 1,000 tickets sold at $3.00 each. What is Melinda\'s expectation?

Solution

Follwoing table shows the calculation for finding expectation:

First column shows the possible outcomes on the tickets. First number shows the outcome on the first ticket and second on the second ticket. Here N shows no prize.

Second column shows the total amount winning minus $6 (cost prize of the tickets). This column shows the possible values which random variable can take.

Third and fourth column shows the probability of X. There are total 7 tickets out of 1000 in which she can buy prize. Rest 993 have no prize.

Fifth column shows multiplication of x and p(x). Its total gives us required expectation. Hence, required expected value of Melinda\'s is -$2.