Probability (part 8)

TL;DR

Bayes' theorem shows that if we flip a coin 5 times and get 5 heads, there is a 32/41 chance that we picked the two-sided coin.

Transcript

So in the last video I hopefully proved to you, at least maybe it doesn't make intuitive sense just yet, but I showed you that the probability of a and b is equal to the probability of a given b times the probability of b. And the probability of b given a is equal to the probability of b given a times a. And then we played around a little bit and w... Read More

Key Insights

• ❓ Bayes' theorem can be applied to calculate conditional probabilities.
• ❓ The probability of an event given another event can be found using Bayes' theorem.
• 🆘 Visual representations can help understand the concepts of Bayes' theorem.

Questions & Answers

Q: What is Bayes' theorem and how is it applied in this context?

Bayes' theorem is a formula that calculates conditional probabilities. In this context, it is used to find the probability of picking the two-sided coin given 5 heads in 5 flips.

Q: What is the probability of getting 5 heads given the two-sided coin?

The probability of getting 5 heads given the two-sided coin is 1, as it is guaranteed to happen with the two-sided coin.

Q: What is the probability of picking the two-sided coin?

The probability of picking the two-sided coin is 1/10, as there are 10 coins in the bag and one of them is two-sided.

Q: What is the probability of getting 5 heads in general?

The probability of getting 5 heads in general is 41/320, which was calculated in a previous problem.

Summary & Key Takeaways

• The previous video introduced Bayes' theorem, which states that the probability of two events happening together is the product of their individual probabilities.

• To find the probability of picking a two-sided coin given 5 heads in 5 flips, Bayes' theorem is applied.

• The probability of getting 5 heads given the two-sided coin is 1, the probability of picking the two-sided coin is 1/10, and the probability of getting 5 heads in general is 41/320.