1000 raffle tickets are sold at $3 each. One grand prize of $100 and two consolation prizes of $75 will be awarded. Find Jake’s expectation if he purchases one ticket.
A) -$2.75 B) -$3.00 C) $0.24 D) $2.75 E) $3.00
There are three possibilities:
1. Jake wins the grand prize of $100, but since he
paid $3, that amounts to winning only +$97.
2. Jake wins one of the two consolation prizes of $75,
but since he paid $3, that amounts to winning +$72.
3. Jake wins 0$, and since he paid $3, that amounts to
losing $3, which can be thought as "winning" -$3.
(Losing is considered "winning" a negative number
of dollars.)
The probability that 1 will occur is 1/1000 or 0.001
The probability that 2 will occur is 2/1000 or 0.002
The probability that 3 will occur is 997/1000 or 0.997
Winnings: Probability Winnings × Probability
X P X × P
1. +$97 | 0.001 | $97 × 0.001 = +$0.097
2. +$72 | 0.002 | $72 × 0.002 = +$0.144
3. -$3 ! 0.997 | -$3 × 0.997 = -$2.991
-----------------------------------------------------
Totals: 1.000 -$2.75
The concept is this: If this same raffle were held
many times, then if Jake bought one ticket every time,
and counted up all his winnings and losses, he would
average losing $2.75 per game, and this is considered
to be the negative number -$2.75.
Edwin
