A friend of yours, Phil, writes to you asking about a new scratch-off lottery game. It costs $10 to play this game. There are two outcomes for the game (win, lose) and the probability that a player wins a game is 60%. A win results in $15, for a net win of $5.
The probability distribution for \(X =\) the amount of money a player wins (or loses) in a single game is as follows:
\(X\) | Probability of \(X\) |
---|---|
+$5 | .60 |
-$10 | .40 |
Phil:
Regarding your idea that you should play this new lottery game many, many times to make some extra money, I thinkā¦
Commentary
The purpose of this task is to have students compute and interpret an expected value, and then use the information provided by the expected value to make a decision. The task is designed to encourage students to communicate their findings in a non-technical form in context, ideally convincing Phil not to go through with his strategy of playing the game many, many times.
After students have had a chance to write a response in part (b), you might want to have students engage in a small group or whole class discussion where responses are shared and critiqued. Then students can be given an opportunity to revise their repsonses in part (b) to stengthen them based on the discussion.
Note: the outcomes above occurs when a ticket costs $10 and a winning ticket says "You win $15." As an extension of the task, students may want to consider the potential popularity of a $10 scratch-off lottery game that is advertised as "Over half the tickets are $15 winners!"