A $5 discount coupon is provided to N riders, with a probability of P for each coupon being utilized. What is the anticipated cost for the company?

This inquiry pertains to the application of probability theory. The company has distributed N coupons, each with a probability P of being utilized. They need to determine their expected cost, which represents the expense incurred if every coupon is redeemed. The expected cost is computed using a formula: Expected Cost = total number of occurrences * probability of occurrence * event cost. In this context, Total number of occurrences refers to the quantity of coupons issued (N), Probability of occurrence signifies the likelihood of each coupon being used (P), and Event cost represents the cost associated with each event (the specified cost of a coupon, which is $5)

The company's anticipated cost is determined by multiplying the total number of coupons by the likelihood of their use, and then by the cost per event, which in this scenario is the cost per coupon. Thus, Expected cost = N * P * $5. For example, if N = 1000 (meaning 1000 coupons have been distributed) and P = 0.1 (indicating a 10% probability of coupon usage), the expected cost for the company would be 1000 * 0.1 * $5 = $500.

Using the formula Expected cost = N * P * 5 dollars, if the company distributes N = 2000 coupons and the probability of each coupon being used is P = 0.05 (5%), the expected cost can be determined as follows: Expected cost = 2000 * 0.05 * $5 = $500. For example, based on these calculations, the company should anticipate a cost of around $500 if they issue 2000 coupons with a 5% usage probability.