12.4 Expected Value

• The expected value is the long run average profit or loss from an activity.
• You can use expected value to predict how playing a game will pay off in the long run
• E = P₁ A₁ + P₂ A₂ + ... + P_n A_n
• Where P_i is the probability that event i will occur.
• and A_i is the profit or loss if event i occurs.
• The entire sample space must be covered by the selected events.
• The fair price is the expected value plus the cost to play.
• Some examples:
  • The Nursing and Allied Health fair is expected to draw 50 people if it does not rain and 65 if it does. There is a 40% chance of rain. What is the expected number of people who will attend the fair?
  • At the Royal Dragon Chinese restaurant, a slip in the fortune cookie indicates the discount. A bag of ten cookies contains seven $1 off, two $2 off and one $5 off. What is the expected discount?
  • Mike and Dave play a game. Mike picks a card from the deck. If it is club, Dave gives him $4, if not, he gives Dave $2. What is Mike's Expected Value, what is Dave's expected value?
  • Five hundred raffle tickets are sold for $3 each. One prize of $500 will be given. What is the expected value of a ticket? What is the fair price.
  • Ten thousand raffle tickets are sold for $5 each. One prize of $%00, one prize of $2500 and two prizes of $1000 are given. What is the expected value of a ticket?
  • According to the life insurance company the probability that a 20 year old woman will dies in one year is .006. What is the expected value of a $10,000 1-year insurance policy that costs $100?