Question

A grocery store manager notes that 35% of the customers who buy a product make use of a store coupon to receive a discount. If seven people purchase the product, what is the probability that fewer than four will use a coupon? use 2 decimal places

Answer 1

To find the probability that fewer than four out of seven customers will use a coupon with a 35% probability of coupon use, calculate the binomial probability for each case of 0, 1, 2, and 3 users, then sum those probabilities.

Step-by-step explanation:

You're asking about the probability that fewer than four people will use a coupon when purchasing a product, given that 35% of customers use a coupon. This is a binomial probability problem because each purchase can be thought of as a trial with two outcomes: either a coupon is used or not. The probability 'p' of using a coupon is 0.35, while the probability 'q' of not using a coupon is 0.65 (since q = 1 - p).

To find the probability that fewer than four out of seven people will use a coupon, you would calculate the sum of the probabilities for exactly 0, 1, 2, and 3 people using a coupon. This can be done using the binomial probability formula:

For exactly x people, the formula is:

P(X = x) = (nCx) * (p^x) * (q^(n-x))

Where n = total number of trials (7 people), p = probability of success (0.35), q = probability of failure (0.65), and x is the number of successes (number of people using a coupon) which in this case we calculate separately for each scenario of 0, 1, 2, and 3 out of 7.

After calculating each of these probabilities, you would add them up to get the total probability that fewer than four will use a coupon.