# A $5 discount coupon is given to N riders. The probability of using a coupon is P. What is the expected cost for the company?

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# A $5 discount coupon is given to N riders. The probability of using a coupon is P. What is the expected cost for the company?

**Category:**
**Asked at:** Lyft
**Difficulty:**

## Question Explanation

This question is essentially a probability theory application. The company has given out N coupons, and each coupon has a probability P of being used. The company needs to calculate their expected cost, which would be the cost should each coupon be used. It is calculated using a formula: Expected Cost = total no. of occurrences * probability of occurrence * event cost. In this case, Total no. of occurrences is the number of coupons given out �N�, Probability of occurrence is the chance of each coupon getting used �P�, and Event cost is the cost of each event (the given cost of a coupon, which is $5�

## Answer Example 1

The expected cost for the company is calculated as the total number of coupons multiplied by the probability of their usage, then multiplied by the cost per event, which in this case is the cost per coupon. So, Expected cost = N � P � $5. For instance, if N � 1000 (i.e. 1000 coupons have been given out) and P � 0.1 (i.e. there is a 10% chance of coupon usage), the expected cost for the company would be 1000 � 0.1 � $5 � $500.

## Answer Example 2

Following the equation Expected cost = N � P � 5 dollars, if the company gives away N � 2000 coupons, and known probability of each coupon to be used P � 0.05 �5%�, the expected cost can be calculated as follows: Expected cost = 2000 � 0.05 � $5 � $500. For instance, with these figures, the company can expect an approximate cost implication of $500 if they distribute 2000 coupons with a usage probability of 5%. 1Share