The Price is Right (Part 2)

Pathfinder Game

            Contestants stand in the middle of a five by five grid of numbers and are given the first number in the price of a car, which they stand on. They then have four choices for the 2nd number in the car, three choices for the 3rd number, two or three choices for the 4th number depending on the show, and two choices for the 5th number. Contestants also have the opportunity to win three more guesses by knowing the price of three smaller prizes. Students are asked if they think it is easier to win a car in this game or the temptation game (see the blog post below for the temptation game).  If students need more guidance the following questions could be used to help students determine which game is the better chance to win a car. 

1. What is the probability of correctly guessing the 2nd number of the price of the car?
2. What is the probability of correctly guessing the 3rd number of the price of the car?
3. What is the probability of correctly guessing the 4th number of the price of the car?
4. What is the probability of correctly guessing the 5th number of the price of the car?
5. What is the probability of correctly guessing in a row the 2nd, 3rd, 4th, and 5th number of the price of the car?
6. If a contestant were able to have three additional guesses, what would be the probability of correctly guessing all of the numbers of the price of the car?
7. Is it likely that a contestant would guess the correct price of all three smaller prizes?
8. Is it more likely to win a car in the Temptation game or the Pathfinder game?

​Punch a Bunch Game
        In this game, contestants can earn up to four chances to punch on a fifty-hole punchboard arranged in five rows of ten. Contestants earn chances by being shown a price for a prize and correctly stating if the actual price is higher or lower than the price shown. Each hole on the punchboard has a value from $25000 down to $100 and there is a certain amount of each value. After seeing the amount in one punched hole, contestants can keep the money or go on to see what value is in another punched hole. 

Students answer the following questions on probability and expected value to determine the best strategy for playing this game.

1. What is the probability of winning each money amount with one punch?
2. Which amount has the greatest probability? The least?
3. What is the expected value for this game with one punch?
4. Suppose a contestant has passed on $1000 and $500. They get $2500 on their third punch. Should they keep this or see what value is in their fourth punch?

Reference
Stohlmann, M. (2018). The math is right! The Australian Mathematics Teacher, 74(3), 9-14.