Question

On the TV game show The Price Is Right, contestants play games to try to win prizes. One of these games is called “Let ‘Em Roll.” In this game, players roll five 6-sided dice. These dice each have 3 faces labeled with a car; the other 3 faces are labeled with prize money amounts (one each of $500, $1,000, and $1,500). Players get to roll all 5 dice, and then have the opportunity to win additional rolls. If all 5 dice show a car, the contestant wins a new car. If not, the contestant can use any additional rolls to reroll the dice with prize money showing to try to win the car (or, they can take the total amount of money showing on the dice and end the game). Josh is playing this game, and he has 2 rolls total (these are the two stages of the experiment; the number of cars showing on the dice will be the reported outcome of each stage).

(please help I don't understand what this us asking for I know samples are wrote as like S={1C,2C,3C,4M,5M,6M} but I need help with figuring out rolls two and three.)

Answer 1

It seems like you're trying to understand the game "Let 'Em Roll" and how to calculate probabilities for different outcomes in the game. You've already defined a sample space for the first roll, which is a good start. Let me help you with the second and third rolls.

In the game "Let 'Em Roll," there are two main stages: the initial roll and subsequent rolls. Here's how you can calculate probabilities for the second and third rolls:

1. First Roll:
- You correctly defined the sample space for the first roll: S = {1C, 2C, 3C, 4M, 5M, 6M}.
- C represents a car, and M represents prize money amounts.

2. Second Roll:
- After the first roll, you need to consider the outcomes that didn't result in all cars (1C, 2C, 3C) because if you roll all cars, you win instantly.
- So, for the second roll, the sample space would be the outcomes with prize money amounts (4M, 5M, 6M).
- Calculate the probabilities for each outcome in the second roll, taking into account the remaining dice.

3. Third Roll (if needed):
- Similarly, if you didn't win a car in the second roll, you proceed to the third roll.
- Again, consider only the outcomes with prize money amounts from the second roll's results (e.g., if you got 4M in the second roll, you'll roll the dice again with only those dice labeled 4M).
- Calculate the probabilities for each outcome in the third roll.

Keep in mind that the probabilities for each roll depend on the outcomes of the previous rolls, as you're only rerolling the dice with prize money amounts, not all five dice.

If you have specific outcomes or probabilities you'd like help with, please provide more details, and I can assist you further.