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Simulation to Predict Probability
Suppose a basketball player typically makes five out of eight foul shots.
Question 1
How could a single foul shot be simulated?
Responses
A Place five red marbles to represent as shot made and five blue marbles to represent a shot missed in a bag. Randomly pull a marble out of the bag to represent one attempt at a foul shot.Place five red marbles to represent as shot made and five blue marbles to represent a shot missed in a bag. Randomly pull a marble out of the bag to represent one attempt at a foul shot.
B Place three red marbles to represent as shot made and five blue marbles to represent a shot missed in a bag. Randomly pull a marble out of the bag to represent one attempt at a foul shot.Place three red marbles to represent as shot made and five blue marbles to represent a shot missed in a bag. Randomly pull a marble out of the bag to represent one attempt at a foul shot.
C Place three red marbles to represent as shot made and three blue marbles to represent a shot missed in a bag. Randomly pull a marble out of the bag to represent one attempt at a foul shot.Place three red marbles to represent as shot made and three blue marbles to represent a shot missed in a bag. Randomly pull a marble out of the bag to represent one attempt at a foul shot.
D Place five red marbles to represent as shot made and three blue marbles to represent a shot missed in a bag. Randomly pull a marble out of the bag to represent one attempt at a foul shot.Place five red marbles to represent as shot made and three blue marbles to represent a shot missed in a bag. Randomly pull a marble out of the bag to represent one attempt at a foul shot.
Question 2
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.
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 shots.
Question 1:
A: Place five red marbles to represent a shot made and five blue marbles to represent a shot missed in a bag. Randomly pull a marble out of the bag to represent one attempt at a foul shot.
Question 2:
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 shots.
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 shots.
Question 1:
To simulate a single foul shot, you would need to represent the player's accuracy, which in this case is making 5 out of 8 shots. One way to do this is by using marbles.
You would place five red marbles to represent shots made and five blue marbles to represent shots missed in a bag. Then, you would randomly pull a marble out of the bag to simulate one attempt at a foul shot.
Therefore, the correct answer is A: Place five red marbles to represent a shot made and five blue marbles to represent a shot missed in a bag. Randomly pull a marble out of the bag to represent one attempt at a foul shot.
Question 2:
To predict the probability of the player making at least one shot out of 3 foul shot attempts, you would carry out trials and count the number of successful attempts.
In this case, you randomly pull marbles out of the bag to represent the attempts. One way to do this is by carrying out 30 trials, where 3 marbles are randomly pulled out of the bag with replacement each time. With replacement means that after each pull, the marble is put back into the bag, so the probabilities remain the same for each trial.
To estimate the probability of making at least one shot out of 3 foul shot attempts, you count the number of successful attempts (shots made) in the 30 trials and divide that number by 30.
Therefore, the correct answer is A: Carry out 30 trials where 3 marbles are randomly pulled out of the bag with replacement each time. Count the number of successes and divide by 30 to estimate the probability of making at least one shot out of 3 foul shots.