Question

a lottery posted the probabilities of winning each prize and the prize amounts as shown in the chart to the right. suppose that one lottery ticket costs \\$1. find the expected value of the winnings for a single ticket. then state how much you can expect to win or lose each year if you buy 10 lottery tickets per week? should you actually expect to win or lose this amount? explain.

\

$$\begin{array}{|c|c|} \\hline \\text{prize} & \\text{probability} \\\\ \\hline \\$1,000,000 & 1 \\text{ in } 40,000,001 \\\\ \\$100,000 & 1 \\text{ in } 20,000,001 \\\\ \\$1000 & 1 \\text{ in } 10,000,001 \\\\ \\hline \\end{array}$$

the expected value of the winnings for a single ticket is \\$-0.97.
(round to the nearest cent as needed.)

if you buy 10 tickets per week, you can expect to lose/win \\$ each year.
(round to the nearest cent as needed.)

Explanation:

Calculate annual tickets purchased

Using the Expected Value knowledge point

$$ \text{Tickets per year} = 10 \text{ tickets/week} \times 52 \text{ weeks/year} = 520 \text{ tickets/year} $$

Determine annual expected value

Using the Lottery Expected Value knowledge point

$$
LATEXBLOCK0
$$

Since the expected value is negative, this represents an expected loss of \(\$504.40\) each year.

Answer:

If you buy 10 tickets per week, you can expect to <blank>lose</blank> <blank>\$504.40</blank> each year.