Dependent probability example | Probability and Statistics | Khan Academy

TL;DR

The video explains how to calculate the probability of getting two heads in a row when randomly selecting a coin from a bag that contains both fair and unfair coins.

Transcript

You have eight coins in a bag. Three of them are unfair in that they have a 60% chance of coming up heads when flipped. The rest are fair coins. So if three or unfair, the rest are eight coins. When this problem says that they are fair coins, it means that they have a 50/50 chance of coming up either heads or tails. You randomly choose one coin fro... Read More

Key Insights

• 🪙 Unfair coins have a higher probability of coming up heads than fair coins.
• 🪙 The probability of choosing a fair coin is higher than choosing an unfair coin from the bag.
• 🪙 The calculation involves multiplying the probabilities of choosing a certain coin type and the probability of getting two heads for that coin.

Questions & Answers

Q: How many coins are in the bag, and how many of them are unfair?

There are eight coins, out of which three are unfair with a 60% chance of coming up heads.

Q: What is the difference between fair and unfair coins?

Fair coins have a 50% chance of heads or tails, while unfair coins have a 60% chance of coming up heads.

Q: How is the probability of choosing a fair coin calculated?

There are five fair coins out of the total eight, so the probability of choosing a fair coin is 5/8.

Q: What is the probability of getting two heads in a row given a fair coin?

If we know the coin is fair, the probability of getting two heads in a row is 25% or 0.25.

Q: What is the probability of choosing an unfair coin and getting two heads in a row?

The probability is 3/8 multiplied by 0.36, which equals 0.135.

Q: How is the final probability of getting two heads calculated?

The probabilities of choosing a fair coin and an unfair coin with two heads are added together, resulting in approximately 29.13%.

Summary & Key Takeaways

• There are eight coins in a bag, with three being unfair and having a 60% chance of coming up heads, while the rest are fair coins with a 50% chance.

• To calculate the probability of getting two heads, a decision tree is created, considering the probabilities of choosing a fair or unfair coin and the respective probabilities of getting two heads for each type of coin.

• The final probability of getting two heads is approximately 29.13%.