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A lottery has a grand prize of $320,000, four runner-up prizes of $32,000 each, twelve third-place prizes of $8000 each, and twenty-five consolation prizes of $800 each. If 1,600,000 tickets are sold for $1 each and the probability of any one ticket winning is the same as that of any other ticket winning, find the expected return on a $1 ticket. (Round your answer to two decimal places.)

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Answer: -$0.65

Explanation:

Probability of winning the $320,000 = 1 / 1,600,000

Probability of winning the $32,000 = 4 / 1,600,000

Probability of winning the $8,000 = 12 / 1,600,000

Probability of winning the $800 = 25 / 1,600,000

Probability of losing your $1 = (1,600,000 - 25 - 12 - 4 - 1) / 1,600,000 = ‭1,599,958‬ / 1,600,000

Expected return = (1 * 320,000/1,600,000) + (4 * 32,000/1,600,000) + (12 * 8,000/1,600,000) + (25 * 800/ 1,600,000) - ‭(1,599,958‬ * 1 / 1,600,000)

= -0.64747375‬

= -$0.65

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