Simulation to Predict Probability
Suppose a basketball player typically makes five out of eight foul shots.
how could you predict the probability of the player making at least one shot out of 3 foul shot attempts?
Responses
A Carry out 30 trials where 3 marbles are randomly pulled out of the bag with replacement. Count the number of successes and divide by 30 to estimate the probability of making at least one shot out of 3 foul shouts.Carry out 30 trials where 3 marbles are randomly pulled out of the bag with replacement. Count the number of successes and divide by 30 to estimate the probability of making at least one shot out of 3 foul shouts.
B Carry out 30 trials where a marble is randomly pulled out of the bag. Count the number of successes and divide by 30 to estimate the probability of making at least one shot out of 3 foul shouts.Carry out 30 trials where a marble is randomly pulled out of the bag. Count the number of successes and divide by 30 to estimate the probability of making at least one shot out of 3 foul shouts.
C Carry out 30 trials where a marble is randomly pulled out of the bag. Count the number of failures and divide by 30 to estimate the probability of making at least one shot out of 3 foul shouts.Carry out 30 trials where a marble is randomly pulled out of the bag. Count the number of failures and divide by 30 to estimate the probability of making at least one shot out of 3 foul shouts.
D Carry out 30 trials where 3 marbles are randomly pulled out of the bag with replacement. Count the number of failures and divide by 30 to estimate the probability of making at least one shot out of 3 foul shouts.
None of the options presented are correct for predicting the probability of the basketball player making at least one shot out of 3 foul shot attempts. The best option would be to carry out a simulation where the basketball player takes 3 foul shots in each trial, and the outcome of each shot is determined by a random number generator using the player's 5/8 success rate. The simulation can then be run multiple times (e.g. 10,000 trials) to estimate the probability of making at least one shot out of 3.
D - Carry out 30 trials where 3 marbles are randomly pulled out of the bag with replacement. Count the number of failures and divide by 30 to estimate the probability of making at least one shot out of 3 foul shots.
The correct answer is D: Carry out 30 trials where 3 marbles are randomly pulled out of the bag with replacement. Count the number of failures and divide by 30 to estimate the probability of making at least one shot out of 3 foul shots.
To understand why, let's break down the problem and explain the process step by step.
The basketball player typically makes 5 out of 8 foul shots. This means the probability of making a single foul shot is 5/8.
To predict the probability of the player making at least one shot out of 3 foul shot attempts, we can use simulation. In this case, we can use marbles in a bag as a simulation tool. Let's assume there are 8 marbles in the bag, 5 of which are "success" marbles (representing successful shots) and 3 of which are "failure" marbles (representing missed shots).
Now, we can simulate the 3 foul shot attempts by randomly pulling out 3 marbles from the bag with replacement. With replacement means that after each marble is pulled out, it is put back into the bag before the next pull, ensuring that each pull is independent.
In 30 trials, we repeat this process 30 times and count how many of those trials result in 3 misses (pulling out only failure marbles). The number of misses represents the number of trials where the player didn't make at least one shot out of the 3 attempts.
Finally, we divide the number of failures by the total number of trials (30) to estimate the probability of making at least one shot out of 3 foul shots.
To summarize, option D is the correct choice because it correctly describes the simulation process of pulling 3 marbles out of the bag with replacement and counting the number of failures (3 misses) for 30 trials to estimate the desired probability.