Dependent probability example 2 | Probability and Statistics | Khan Academy

TL;DR

What is the probability of getting four heads when randomly choosing a coin with 3 unfair and 1 fair coin in a bag?

Transcript

Let's do another one of these dependent probability problems. You have 4 coins in a bag. 3 of them are unfair in that they have a 45% chance of coming up tails when flipped. The rest are fair. So for the rest of them, you have a 50% chance of tails or a 50% chance of heads. You randomly choose one coin from the bag and flip it 4 times. What is the ... Read More

Key Insights

• 🪙 There are 3 unfair coins and 1 fair coin in the bag.
• 🤕 The unfair coins have a 45% chance of tails and a 55% chance of heads.
• 🤕 The fair coin has a 50% chance of heads and tails.
• 🪙 The probability of getting four heads with the unfair coin is higher than with the fair coin.

Questions & Answers

Q: How many coins are in the bag?

There are a total of 4 coins in the bag, 3 of which are unfair and 1 is fair.

Q: What is the chance of getting an unfair coin?

There is a 3/4 (or 75%) probability of picking an unfair coin from the bag.

Q: What is the probability of getting tails with the unfair coin?

The unfair coin has a 45% chance of coming up tails, which means it has a 55% chance of coming up heads.

Q: What is the probability of getting four heads with the unfair coin?

The probability of getting four heads with the unfair coin is 0.55 to the fourth power or approximately 0.0686.

Q: How likely is it to pick a fair coin?

There is a 1/4 (or 25%) probability of picking a fair coin from the bag.

Q: What is the probability of getting tails with the fair coin?

The fair coin has a 50% chance of coming up tails, which means it also has a 50% chance of coming up heads.

Q: What is the probability of getting four heads with the fair coin?

The probability of getting four heads with the fair coin is 0.5 to the fourth power or 0.0156.

Q: What is the overall probability of getting four heads?

The overall probability of getting four heads, regardless of the type of coin chosen, is approximately 8.43%.

Summary & Key Takeaways

• There are 4 coins in a bag, with 3 unfair coins having a 45% chance of tails and 1 fair coin having a 50% chance of tails.

• When choosing a coin randomly, there is a 3/4 chance of picking an unfair coin and a 1/4 chance of picking a fair coin.

• The probability of getting four heads with the unfair coin is 0.55 to the fourth power, and with the fair coin is 0.5 to the fourth power.