Tyler believes that an 8-sided die can be used to predict whether customers at his store will use a coupon when making their purchases, with a roll of 1 indicating a coupon and all other outcomes indicating no coupon. Today, 4 of the first 48 customers in the store used a coupon. How does the experimental probability of a customer using a coupon compare to the theoretical probability of Tyler’s die?
A. The experimental probability is greater than the theoretical probability by more than 2%.
B. The experimental probability is less than the theoretical probability by more than 2%.
C. The experimental probability is greater than the theoretical probability, but within 2%.
D. The experimental probability is less than the theoretical probability, but within 2%.
To find the experimental probability of a customer using a coupon, we divide the number of customers who used a coupon by the total number of customers:
Experimental probability = 4/48 = 1/12 ≈ 0.0833
The theoretical probability of a customer using a coupon when rolling an 8-sided die is 1/8 = 0.125.
To compare the two probabilities, we calculate the difference:
0.125 - 0.0833 = 0.0417
This is greater than 2%, so the correct answer is:
B. The experimental probability is less than the theoretical probability by more than 2%.