Exactly three heads in five flips | Probability and Statistics | Khan Academy

TL;DR

The video discusses the probability of getting exactly three heads in five coin flips, with a final probability of 5/16.

Transcript

So let's start again with a fair coin. And this time, instead of flipping it four times, let's flip it five times. So five flips of this fair coin. And what I want to think about in this video is the probability of getting exactly three heads. And the way I'm going to think about it is, if you have five flips, how many different equally likely poss... Read More

Key Insights

• 🧚 There are 32 equally likely possibilities when flipping a fair coin five times.
• 🤕 To calculate the number of possibilities for exactly three heads, the permutation of three different heads must be divided by 3 times 2 times 1.
• 🤕 The final probability of getting exactly three heads in five coin flips is 5/16.

Questions & Answers

Q: What is the total number of equally likely possibilities when flipping a fair coin five times?

When flipping a fair coin five times, there are 32 equally likely possibilities.

Q: How many ways are there to get exactly three heads out of these possibilities?

Out of the 32 equally likely possibilities, there are 10 ways to get exactly three heads.

Q: Why do we need to divide the number of possibilities by the number of ways to arrange three different things?

We need to divide the number of possibilities by the number of ways to arrange three different things (3 times 2 times 1) to avoid overcounting and treating different arrangements as separate possibilities.

Q: What is the final probability of getting exactly three heads?

The final probability of getting exactly three heads in five coin flips is 5/16.

Summary & Key Takeaways

• The video explores the probability of getting exactly three heads in five coin flips.

• There are 32 equally likely possibilities when flipping a fair coin five times.

• Out of these possibilities, there are 10 ways to get exactly three heads.