Post Cereals has decided to run a promotion whereby they are

Post Cereals has decided to run a promotion whereby they are putting 10 different Yu-Gi-Oh cards in specially marked boxes of cereal. Card number 3 is the most sought after card in the series.

a. What is the probability that you will get card number 3 without having to buy more than 3 boxes of specially marked cereal? (Assume that all cards are equally likely).

b. Suppose you are unlucky and you don’t get card number 3 in the first 3 boxes you buy. On average, how long will you have to wait to get card number 3?

Solution

A)Because you have 10 different yugioh cards, and all would be equally likely, the chance of getting card 3 is 1/10 or 10%. Since you buy three boxes, the chance is 1/10+1/10+1/10 or 3/10 or 30%.

B) The average time it would take for something to happen is the same as the theoretical probability of 100%. This means the average time it would take is 10 boxes, because 100% = 10/10.