11. congratulations! you are going to be a contestant on a new game show with a chance to win some money…

11. congratulations! you are going to be a contestant on a new game show with a chance to win some money. you will spin the two spinners shown below to see how much money you will win. a. make a tree diagram of all the possible outcomes of spinning the two spinners. at the ends of the branches, on the far right, write the amount you would win for each combination of spins. b. are each of the outcomes in the sample space equally likely?

11. congratulations! you are going to be a contestant on a new game show with a chance to win some money. you will spin the two spinners shown below to see how much money you will win. a. make a tree diagram of all the possible outcomes of spinning the two spinners. at the ends of the branches, on the far right, write the amount you would win for each combination of spins. b. are each of the outcomes in the sample space equally likely?

Answer

Explanation:

Step1: Identify outcomes of first spinner

The first spinner has 3 outcomes: $100, $300, $1500.

Step2: Identify outcomes of second spinner

The second spinner has 2 outcomes: Keep Your Winnings, Double Your Winnings.

Step3: Create tree - diagram branches

For the $100 outcome of the first spinner:

  • If we keep our winnings, we win $100.
  • If we double our winnings, we win $200. For the $300 outcome of the first spinner:
  • If we keep our winnings, we win $300.
  • If we double our winnings, we win $600. For the $1500 outcome of the first spinner:
  • If we keep our winnings, we win $1500.
  • If we double our winnings, we win $3000.

Step4: Determine equal - likelihood

Each spin of the first spinner is equally likely (since the sections seem to be of equal size), and each spin of the second spinner is equally likely. Also, the outcome of the first - spinner spin does not affect the outcome of the second - spinner spin. So, all 3×2 = 6 outcomes in the sample space are equally likely.

Answer:

a. Tree - diagram: Start with three main branches for the first - spinner outcomes ($100, $300, $1500). From each of these branches, create two sub - branches. For the $100 branch, one sub - branch labeled $100 (Keep Your Winnings) and another labeled $200 (Double Your Winnings). For the $300 branch, one sub - branch labeled $300 (Keep Your Winnings) and another labeled $600 (Double Your Winnings). For the $1500 branch, one sub - branch labeled $1500 (Keep Your Winnings) and another labeled $3000 (Double Your Winnings). b. Yes, each of the outcomes in the sample space is equally likely.