A discount coupon is given to N riders. The probability of using a coupon is P. What is the probability that one of the coupons will be used?
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A discount coupon is given to N riders. The probability of using a coupon is P. What is the probability that one of the coupons will be used?
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Question Explanation
In this question, you are given two variables. N riders - This refers to the total number of coupons distributed or available for use. Probability of using a coupon, P - This refers to the likelihood of any given coupon being used. The question is asking, if every rider has the same probability �P) of using their coupon, what is the chance (the probability) that at least one of those N coupons will be used. You must remember that the riders are independent of each other, meaning one rider using a coupon does not affect another rider's decision to use their coupon. The key to answer this question is to understand that the probability of at least one event happening is equal to 1 minus the probability of none of the events happening.
Answer Example 1
The way to calculate this is to firstly find the probability of none of the coupons being used, and then subtract this value from one. The probability of one coupon not being used is �1�P�, so the probability of N coupons not being used is �1�P�^N. Therefore, the probability of at least one coupon being used is 1 - ��1�P�^N�.
Answer Example 2
The calculation for this kind of probability question revolves around understanding the principal of '1 minus the probability of the opposite'. The 'opposite' in this context would be none of the coupons being used. We know that the probability of one coupon not being used is �1�P�, so the outcome for all N coupons is �1�P) raised to the power of N. Now, we subtract this value from 1 to get our answer, so the probability of at least one coupon being used is 1 - �1�P�^N. 0Share
