The Correct Answer and Explanation is:
The correct answer is loss of $1.83.
To determine the expected gain or loss of buying a raffle ticket, we need to calculate the expected value. Expected value represents the average outcome you would expect if you were to play this raffle many times. The calculation involves considering all possible outcomes, their values, and their probabilities.
First, let’s identify the total value of all the prizes available. There is one grand prize worth $100 and five smaller prizes worth $20 each.
Total prize value = (1 × $100) + (5 × $20)
Total prize value = $100 + $100 = $200
Next, we calculate the average prize value per ticket. Since there are 1,200 tickets sold in total, we can find the average value by dividing the total prize money by the total number of tickets. This figure represents the expected winnings for a single ticket before considering its cost.
Average prize value per ticket = Total prize value / Total number of tickets
Average prize value per ticket = $200 / 1,200
Average prize value per ticket ≈ $0.1667
Now, to find the expected gain or loss, we must subtract the cost of the ticket from this average prize value. Each ticket costs $2.
Expected gain/loss = Average prize value per ticket – Cost of ticket
Expected gain/loss = $0.1667 –
2.00Expectedgain/loss=–2.00Expectedgain/loss=–1.8333
The result is a negative number, which indicates an expected loss. When rounded to the nearest cent, the expected loss for buying one ticket is $1.83. This means that, on average, for every ticket purchased, a person can expect to lose approximately $1.83. While some people will win prizes and have a significant gain, the vast majority will lose the $2 they spent, leading to this average outcome.
