Binomial distribution | Probability and Statistics | Khan Academy

TL;DR

The video explains how to calculate the probability of getting a certain number of heads when flipping a coin five times.

Transcript

• [Voiceover] Let's define a random variable x as being equal to the number of heads, I'll just write capital H for short, the number of heads from flipping coin, from flipping a fair coin, we're gonna assume it's a fair coin, from flipping coin five times. Five times. Like all random variables this is taking particular outcomes and converting them... Read More

Key Insights

• #️⃣ A random variable can represent different outcomes as numbers.
• 🐬 The total number of outcomes from flipping a coin five times is 32.
• 🤕 The probability distribution for the number of heads follows a symmetric pattern.
• ❓ Combinatorics, specifically binomial coefficients, can be used to calculate probabilities in this scenario.
• 🤲 The probability of getting zero heads is the same as getting zero tails.

Questions & Answers

Q: How many possible outcomes are there from flipping a fair coin five times?

There are 32 equally likely possible outcomes from flipping a coin five times.

Q: What is the probability of getting no heads (x = 0) in five coin flips?

The probability of x = 0 is 1/32, as there is only one outcome (five tails) out of the 32 equally likely possibilities.

Q: How do you calculate the probability of getting one head (x = 1) in five coin flips?

The probability of x = 1 is 5/32. There are five outcomes where one head occurs, and there are 32 equally likely possibilities in total.

Q: What is the probability of getting two heads (x = 2) in five coin flips?

The probability of x = 2 is 10/32. There are ten outcomes where two heads occur, and there are 32 equally likely possibilities in total.

Q: How can you calculate the probability of getting three heads (x = 3) in five coin flips?

The probability of x = 3 is also 10/32. By choosing three out of the five flips to be heads, there are ten possibilities, and there are 32 equally likely outcomes in total.

Q: What is the probability of getting four heads (x = 4) in five coin flips?

The probability of x = 4 is 5/32. By choosing four out of the five flips to be heads, there are five possibilities, and there are 32 equally likely outcomes in total.

Q: What is the probability of getting five heads (x = 5) in five coin flips?

The probability of x = 5 is 1/32. There is only one outcome (five heads) out of the 32 equally likely possibilities.

Summary & Key Takeaways

• A random variable, denoted as x, represents the number of heads obtained from flipping a fair coin five times.

• There are 32 equally likely possible outcomes from flipping a coin five times.

• The probability of x being equal to zero, one, two, three, four, or five can be determined using combinatorics.