Question

Michael finds that 3/5 customers at his grandfather's grocery store use a coupon.

To simulate the behavior of the next 5 customers, he writes the numbers 1, 2, 3, 4, and 5 on cards and mixes them up. He writes down that 1, 2, and 3 represent someone using a coupon and 4 and 5 represent someone not using a coupon.

Michael then randomly selects a card, puts it back, and records the number. He repeats this 5 times to represent 5 customers or 1 trial.

He repeats this experiment for a total of 15 trials. The results are shown in this list.

43454, 24511, 55555, 43453, 55315,25215, 32235, 43311, 11154, 13342,42514, 13223, 44215, 45313, 13324

Using this simulation, what is the probability that, out of the next 5 customers, 4 or more will use a coupon?

Enter your answer, as a fraction in simplified form, in the box.

Answer 1

To find the probability that out of the next 5 customers, 4 or more will use a coupon, we need to analyze the results of the simulation.

Given the results of the 15 trials: 43454, 24511, 55555, 43453, 55315, 25215, 32235, 43311, 11154, 13342, 42514, 13223, 44215, 45313, 13324

We can count the number of trials where 4 or more customers used a coupon. Looking at the list, we can see that the following trials meet this condition: 55555, 55315, 44215, 45313.

There are 4 trials that satisfy the condition. To calculate the probability, we divide the number of trials where 4 or more customers used a coupon (4) by the total number of trials (15):

Probability = Number of favorable outcomes / Total number of outcomes

Probability = 4 / 15

The probability, as a fraction in simplified form, is 4/15.

Therefore, the probability that out of the next 5 customers, 4 or more will use a coupon is 4/15.