Question

1. sales the owner of a hair salon advertises that on the first day of each month, the first 6 customers will receive one of the coupons shown at the right for a discount off their total bill. each coupon is given at random to a different customer.

a. what is the probability that the first customer on may 1 gets the 10% discount and the second customer gets the 25% discount? explain your answer using favorable and possible outcomes.

Explanation:

Step1: Determine total coupons

There are 6 coupons (5% OFF, 10% OFF, 15% OFF, 20% OFF, 25% OFF, 50% OFF), so total possible outcomes for first customer: 6.

Step2: Probability first customer gets 10% OFF

Favorable outcomes for first customer (10% OFF) is 1. So probability \( P_1=\frac{1}{6} \).

Step3: Probability second customer gets 25% OFF (after first)

After first customer takes 10% OFF, 5 coupons left. Favorable outcomes for second customer (25% OFF) is 1. So probability \( P_2=\frac{1}{5} \).

Step4: Multiply probabilities (independent sequential events)

Total probability \( P = P_1\times P_2=\frac{1}{6}\times\frac{1}{5}=\frac{1}{30} \).

Answer:

The probability is \(\frac{1}{30}\).