Question

coupon value number of coupons 10% off 525 20% off 225 30% off 50 which expression shows how to find the probability that the first three customers to enter the store each receive a coupon for 30% off? a. \\(\frac{50}{800} + \frac{50}{800} + \frac{50}{800}\\) b. \\(\frac{50}{800} + \frac{49}{799} + \frac{48}{798}\\) c. \\(\frac{50}{800} \cdot \frac{50}{800} \cdot \frac{50}{800}\\) d. \\(\frac{50}{800} \cdot \frac{49}{799} \cdot \frac{48}{798}\\)

Explanation:

Step1: Calculate total coupons

Total coupons = 525 + 225 + 50 = 800.

Step2: Probability for first customer

Probability first gets 30% off: $\frac{50}{800}$.

Step3: Probability for second customer

After one 30% coupon used: $\frac{49}{799}$.

Step4: Probability for third customer

After two 30% coupons used: $\frac{48}{798}$.

Step5: Combine probabilities

Multiply the three probabilities: $\frac{50}{800} \cdot \frac{49}{799} \cdot \frac{48}{798}$.

Answer:

D. $\frac{50}{800} \cdot \frac{49}{799} \cdot \frac{48}{798}$