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Expected Lotto winnings. Most states offer weekly
Chapter 4, Problem 36E(choose chapter or problem)
Expected Lotto winnings. Most states offer weekly lotteries to generate revenue for the state. Despite the long odds of winning, residents continue to gamble on the lottery each week. In SIA, Chapter 3 (p. 128), you learned that the chance of winning Florida’s Pick-6 Lotto game is 1 in approximately 23 million. Suppose you buy a $1 Lotto ticket in anticipation of winning the $7 million grand prize. Calculate your expected net winnings. Interpret the result.
Questions & Answers
QUESTION:
Expected Lotto winnings. Most states offer weekly lotteries to generate revenue for the state. Despite the long odds of winning, residents continue to gamble on the lottery each week. In SIA, Chapter 3 (p. 128), you learned that the chance of winning Florida’s Pick-6 Lotto game is 1 in approximately 23 million. Suppose you buy a $1 Lotto ticket in anticipation of winning the $7 million grand prize. Calculate your expected net winnings. Interpret the result.
ANSWER:Step 1 of 2
Given that despite the long odds of winning, residents continue to gamble on the lottery each week. And we observe that the chance of winning Florida’s Pick-6 Lotto game is 1 in approximately 23 million.
Suppose we buy a $1 Lotto ticket in anticipation of winning the $7 million grand prize.
The chance of winning Florida’s Pick-6 Lotto game is \(=\frac{1}{23}\) millions.
The price of Lotto ticket is = $1.
The grand price = $7.
The chance of winning is = $7 - $1
The chance of losing is = -$1
The random variable x takes values $7 - $1, -$1.
\(\begin{array}{ccc}
\hline x & \$ 7-\$ 1 & -\$ \\
p(x) & \frac{1}{23} \text { million } & 1-\frac{1}{23} \text { million } \\
\hline
\end{array}\)