Final answer:
The question cannot be directly answered with certainty due to the random nature of the probability. To simulate, one would assign numbers to each probability range and randomly select numbers until one of each card type is obtained, then repeat the process many times to find an average number of boxes needed.
Step-by-step explanation:
The question is asking how many cereal boxes one would need to purchase in order to collect one trading card of each athlete mentioned. As we're dealing with percentages here, this statistical problem falls into the category of probability simulation, where we aim to find an expected value based on given probabilities.
Let's start with the information that we have:
- 20% chance of getting a Tiger Woods card
- 30% chance of getting a David Beckham card
- 50% chance (the remaining percentage) of getting a Michael Phelps card
Since simulation involves randomness and independent events, we cannot state a direct number of cereal boxes that must be bought with absolute certainty. The first card you get has a 100% chance of being a new one, but it becomes more complicated as you collect more cards.
In theory, the least number of boxes you'd need to buy is three: one box that has Tiger Woods, one that has David Beckham, and one that has Michael Phelps. However, since it is random whether you'll get a different card in each box, most likely you will need to buy more than three.
To simulate the process, let's assign the following numbers to represent the probabilities:
- Numbers 1-20 represent getting a Tiger Woods card
- Numbers 21-50 represent getting a David Beckham card
- Numbers 51-100 represent getting a Michael Phelps card
We randomly pick numbers (simulating buying boxes) and count the number of picks until we get at least one of each type of card. Typically, this process is repeated multiple times (perhaps hundreds or thousands) to find an average number of purchases required. This average would then represent the simulation practice result for the number of boxes likely to be needed.
Note: Since real life doesn't operate with neatly divisible probabilities, the result of a simulation only provides an estimate rather than a precise prediction.