Questions: In a state's Pick 3 lottery game, you pay 1.29 to select a sequence of three digits (from 0 to 9), such as 355. If you select the same sequence of three digits that are drawn, you win and collect 353.37. Complete parts (a) through (e). a. How many different selections are possible? 1000 b. What is the probability of winning? 0.001 (Type an integer or a decimal.) c. If you win, what is your net profit? 352.08 (Type an integer or a decimal.) d. Find the expected value. (Round to the nearest hundredth as needed.)

In a state's Pick 3 lottery game, you pay 1.29 to select a sequence of three digits (from 0 to 9), such as 355. If you select the same sequence of three digits that are drawn, you win and collect 353.37. Complete parts (a) through (e). a. How many different selections are possible? 1000 b. What is the probability of winning? 0.001 (Type an integer or a decimal.) c. If you win, what is your net profit? 352.08 (Type an integer or a decimal.) d. Find the expected value. (Round to the nearest hundredth as needed.)
Transcript text: In a state's Pick 3 lottery game, you pay $\$ 1.29$ to select a sequence of three digits (from 0 to 9 ), such as 355 . If you select the same sequence of three digits that are drawn, you win and collect $\$ 353.37$. Complete parts (a) through (e). a. How many different selections are possible? 1000 b. What is the probability of winning? 0.001 (Type an integer or a decimal.) c. If you win, what is your net profit? $\$ 352.08$ (Type an integer or a decimal.) d. Find the expected value. $\$$ $\square$ (Round to the nearest hundredth as needed.)
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Solution

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Solution Steps

Step 1: Number of Different Selections Possible

The total number of different selections possible is calculated as $10 \times 10 \times 10 = 1000$.

Step 2: Probability of Winning

The probability of winning is the reciprocal of the number of different selections possible, which is $\frac{1}{1000}$.

Step 3: Net Profit if You Win

The net profit if you win is calculated by subtracting the amount bet from the amount collected, which is $Y - X = 352.08$ dollars.

Step 4: Expected Value for a $X Bet

The expected value is calculated as $EV = \left(\frac11000 \times (Y - X)\right) + \left(\frac9991000 \times (-X)\right) = -0.94$.

Final Answer:

The expected value for a bet of $1.29 is $-0.94.

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