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At a raffle, 1500 tickets are sold at $2 each. There are four prizes given for $500, $250, $150, and $75. You buy one ticket. Use a probability distribution table to calculate the expected value of your gain. Your expected value is:

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Answer:

The expected value of every ticket is a loss of $ 1.35

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Number of tickets sold at the raffle = 1,500

Price of each ticket = $ 2

Total prizes = 1 * $ 500 + 1 * $ 250 + 1 * $ 150 + 1 * $ 75

2. Use a probability distribution table to calculate the expected value of your gain. Your expected value is_____ ?

Let's answer the question using a probability distribution for the gains, this way:

  • Probability of 1st prize of $ 498 (500 - ticket) = 1/1,500
  • Probability of 2nd prize of $ 248 (250 - ticket) = 1/1,500
  • Probability of 3rd prize of $ 148 (150 - ticket) = 1/1,500
  • Probability of 4th prize of $ 73 (75 - ticket) = 1/1,500
  • Probability of losing $ 2 (ticket) = 1,496/1,500

Now, we calculate the mean for all the tickets (winners and non-winners), this way:

Expected value = [(1,496 * -2) + (1 * 498) + (1 * 248) + ( 1 * 148) + ( 1 * 73)]/1,500

Expected value = [- 2,992 +498 + 248 + 148 + 73)/1,500

Expected value = -2,025/1,500 = - 1,35

The expected value of every ticket is a loss of $ 1.35

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