### Home > CCA2 > Chapter Ch11 > Lesson 11.2.3 > Problem11-67

11-67.

The Algiers High School booster club is planning a fund-raiser to collect money for a new synthetic turf field and stadium lights. The football field is $100 × 53\frac { 1 } { 3 }$ yards. They cover it completely with playing cards ($2.5 × 3.5$ 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 face-down cards on the field.

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

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

$1$ yard = $3$ feet = $36$ inches
How many cards will it take to cover the field?

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 could lose in this fundraiser?

How many packs of playing cards will the boosters need to buy?
How much will this cost? Note: If no one plays, the million dollars is not paid out.

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

The maximum occurs when all cards are purchased, but the booster club will still have to pay for all of the cards and the million dollar prize.

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?

On average, half of the cards will be sold before there is a winner.

5. A state Mega 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?

$\frac{\text{176 million}}{\text{number of cards to cover a football field}}$