Question

Suppose a miniature golf player sinks a hole-in-one about 12% of the time on any given hole and is going to play 8 games at 18 holes each.

Part A: Design a simulation. (Individual work) Design and conduct a simulation to estimate the likelihood that the golfer will sink at least two holes-in-one during a single game. Be sure to show all work for the five steps of simulation.
Part B: Apply your findings. (Individual work)
Using your findings from part A, answer the following questions:
a. What is the probability the golfer got zero or one hole-in-one during a single game?
b. What is the probability the golfer got exactly two holes-in-one during a single game?
c. What is the probability the golfer got six holes-in-one during a single game?​

Answer 1

To estimate the likelihood of sinking at least two holes-in-one during a single game, design and conduct a simulation using the five steps provided. Then, use the findings to calculate the probabilities of getting zero or one holes-in-one, exactly two holes-in-one, and six holes-in-one during a single game.

Step-by-step explanation:

Part A:

To design and conduct a simulation, follow these five steps:

1. Determine the total number of trials: In this case, the golfer is playing 8 games, each with 18 holes, so the total number of trials is 8 * 18 = 144.

2. Define what constitutes a success: In this case, a success is defined as sinking a hole-in-one.

3. Simulate each hole: Generate a random number between 0 and 1 for each hole. If the number is less than or equal to 0.12 (12% probability), count it as a success.

4. Repeat the simulation for all 144 trials.

5. Calculate the number of trials where at least two holes-in-one were sunk and divide by the total number of trials to estimate the likelihood.

Part B:

a. To find the probability of getting zero or one hole-in-one during a single game, subtract the probability of getting at least two holes-in-one (found in Part A) from 1.

b. To find the probability of getting exactly two holes-in-one during a single game, divide the estimated likelihood from Part A by the total number of trials.

c. To find the probability of getting six holes-in-one during a single game, divide the estimated likelihood of getting at least two holes-in-one (from Part A) by the total number of trials.