A certain sweepstakes ticket has four categories of prizes with the following probabilities of being won:
Prize
Probability
$100,000
1/500,000
$50,000
1/250,000
$20,000
1/200,000
$10,000
1/100,000
If each ticket costs $1.00, what is the expected gain or loss?
Select one:
a. $.60
b. $6.00
c. $4.00
d. $.40
Multiply each possible prize times the chance of winning and add them all up. compare that number with $1 to find your expected gain or loss. If the number is larger, you have a gain. If the number is smaller, you have a loss.
the number is larger
To find the expected gain or loss, we need to multiply each prize amount by its probability of being won and subtract the cost of buying the ticket.
Let's calculate the expected gain or loss for each prize:
Expected gain from winning $100,000 = (1/500,000) * $100,000 = $0.20
Expected gain from winning $50,000 = (1/250,000) * $50,000 = $0.20
Expected gain from winning $20,000 = (1/200,000) * $20,000 = $0.10
Expected gain from winning $10,000 = (1/100,000) * $10,000 = $0.10
Now let's sum up the expected gains from each prize:
Total expected gain = $0.20 + $0.20 + $0.10 + $0.10 = $0.60
Since each ticket costs $1.00, we need to subtract the cost of the ticket from the total expected gain:
Expected gain or loss = $0.60 - $1.00 = -$0.40
Therefore, the expected gain or loss is d. -$0.40