# Random number list to run experiment | Probability | AP Statistics | Khan Academy | Summary and Q&A

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July 13, 2017
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Random number list to run experiment | Probability | AP Statistics | Khan Academy

## TL;DR

On average, it takes approximately 11.67 boxes to collect all six prizes in a cereal box lottery.

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### Q: How can Amanda calculate the expected number of boxes she would need to collect on average to win all six prizes?

Amanda can either determine the mathematical expected value or run simulations with random numbers to find the average number of boxes needed.

### Q: How does Amanda simulate collecting boxes to estimate the average number of boxes needed?

Amanda assigns a number to each prize and generates a random string of numbers. She starts from the left and treats each number as a prize. She ignores numbers outside the range of 1-6.

### Q: How many boxes did Amanda need in the first experiment to collect all six prizes?

Amanda needed 8 boxes in the first experiment to collect all six prizes.

### Q: Why does Amanda need to conduct multiple experiments to estimate the average?

Conducting multiple experiments allows for a more accurate estimation of the average number of boxes needed. The more experiments conducted, the closer the average will be to the true theoretical average.

## Summary & Key Takeaways

• Amanda wants to know the average number of boxes she needs to collect to win all six prizes in a cereal box lottery.

• She can approach this question mathematically or by simulating multiple trials with random numbers.

• By running three experiments, she found that the average number of boxes needed to collect all prizes is approximately 11.67.