# L04.6 A Coin Tossing Example | Summary and Q&A

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April 24, 2018
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L04.6 A Coin Tossing Example

## TL;DR

Calculate the probability of the first two coin tosses being heads, given that exactly three out of ten tosses resulted in heads.

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### Q: What is the problem being addressed in this content?

The content addresses the problem of calculating the probability of the first two coin tosses being heads, given that three out of ten tosses resulted in heads.

### Q: What assumptions are made in the probability model?

The model assumes that the coin tosses are independent and that each toss has the same fixed probability (denoted as p) of resulting in heads.

### Q: How is the conditional probability calculated using the first approach?

The conditional probability is calculated by dividing the probability of both events (the first two tosses being heads and having exactly one head in the remaining tosses) by the probability of the conditioning event (exactly three heads in ten tosses).

### Q: How does the second approach utilize the sample space and conditional universe?

The second approach recognizes that, in the conditional universe (given event B occurred), the probability law is uniform. Thus, the desired probability is calculated by counting the number of outcomes that meet the condition and dividing it by the total number of outcomes in the conditioned set.

## Summary & Key Takeaways

• The problem is to calculate the conditional probability of the first two coin tosses being heads, given that there were exactly three heads out of ten tosses.

• Two approaches are developed to solve the problem, one using conditional probabilities and the other utilizing the sample space and conditional universe.

• Both approaches lead to the same solution, with the second approach being slightly easier by directly counting the desired outcomes.