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Home > INT3 > Chapter 8 > Lesson 8.3.2 > Problem 8-118

8-118.
  1. The Algiers High School booster club is planning a fundraiser to collect money for a new synthetic turf field and stadium lights. The boosters will completely cover the football field with playing cards (2.5 inches × 3.5 inches) face down. All the cards are aligned in the same direction as the football field (long side of the card along the long side of the field). There will be exactly one joker card placed at random among the cards on the field. The football field is 100 yards × 53 yards.

    Contestants pay five dollars for every card they wish to turn over. Whoever finds the joker wins one million dollars. Homework Help ✎

    1. What is the probability that the first player finds the joker by turning over one card?

    2. The playing cards used to cover the field cost $0.99 per pack (52 cards per pack). What is the largest amount of money the boosters can lose in this fundraiser?

    3. What is the maximum amount of money the boosters can make?

    4. What is a reasonable expected profit for the booster club? That is, if this fundraiser were done many, many times, what would be the average profit?

    5. A state Mucho Millions lottery advertises odds of 176 million to one. If the state lottery were played like the booster club fundraiser, how many football fields covered with non-joker playing cards would be needed?

If 100 yards = 300 feet = 3600 inches, then 3600 ÷ 3.5 ≈ 1029 cards will fit along the length of the field.
How many cards will fit across the width of the field?

How many packs of cards are needed? What is this cost?
If the first player wins, they pay $5, but win $1,000,000.

In order to get the most money each chance must be purchased, meaning 790,272 people will play.

Assume that on average half the cards will be sold before there was a winner.

$960,633.98