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A lottery has a grand prize of $100,000, two runner-up prizes of $12,500 each, four third-place prizes of $2000 each, and six consolation prizes of $200 each. If 200,000 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.)

Respuesta :

jepessoa

Answer:

$0.66

Explanation:

expected return of a lottery ticket equals the sum of the probabilities of winning each prize:

  • probability of winning $100,000 = 1 / 200,000 = 0.000005 x $100,000 = $0.50
  • probability of winning $12,500 = 2 / 199,999 = 0.000005 x $12,500 = $0.125
  • probability of winning $2,000 = 3 / 199,997 = 0.000005 x $2,000 = $0.03
  • probability of winning $200 = 1 / 199,994 = 0.000005 x $200 = $0.001

total expected value = $0.50 + $0.125 + $0.03 + $0.001 = $0.656 ≈ $0.66

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