Question

400 fundraiser raffle tickets are sold for $20 each for four cash prize amounts: $350, 200, $100, $50. What is the expected value of the payout?

-$18.25
-$18.05
-$1.75
$1.75 (not the answer)

Answer 1

The value of the expected value of payout is $1.75.

What is expected value?

In probability theory, the idea of expected value denotes the typical result of a random event when the event is repeated a lot of times. It is determined by multiplying each potential result by its likelihood before adding together all of these numbers. The anticipated value can shed light on the possible risks and benefits associated with various options or scenarios, making it frequently used to estimate the long-term average of a random process or to make decisions under uncertainty.

To get the payout we need to determine the probability of winning each prize.

For first prize = 1/400

Second prize = 1/400.

Third prize = 1/400.

Fourth prize = 1/400.

The expected value is calculated as:

(1/400) * $350 + (1/400) * $200 + (1/400) * $100 + (1/400) * $50

= $0.875 + $0.50 + $0.25 + $0.125

= $1.75

Hence, the value of the expected value of payout is $1.75.

Explanation:

Answer 2

D: $1.75

Explanation:

To calculate the expected value of the payout, we need to multiply each cash prize amount by the probability of winning that prize and then sum the results.

The probability of winning the $350 prize is 1/400, since there is only one $350 prize and 400 tickets sold. The probability of winning the $200 prize is 1/399, since there is only one $200 prize and one ticket has been removed from the pool of available tickets. Similarly, the probability of winning the $100 prize is 1/398 and the probability of winning the $50 prize is 1/397.

So, the expected value of the payout is:

(1/400) x $350 + (1/399) x $200 + (1/398) x $100 + (1/397) x $50 = $0.875 + $0.501 + $0.251 + $0.126 = $1.753

Therefore, the expected value of the payout is $1.75 (rounded to the nearest cent). So, the answer is D: $1.75.