the "moving left or right" probability problem

TL;DR

The video discusses the probability of a robot returning to the original position after making 10 random moves.

Transcript

okay this is just a really nice continuation from last time where we talk about the northeast let us walk and here's a question for you guys for today suppose we have a robot and you're going to program it each every time he is going to move randomly either to the left or to the right one unit and we will assume that we will have the equal probabil... Read More

Key Insights

• 🧘 The probability of returning to the original position after making 10 random moves is approximately 24.6%.
• 🥺 Different configurations of moves can lead to returning to the original position.
• ↔️ The calculation involves determining the number of ways to get five moves towards the right and five moves towards the left.
• ✊ The total number of possible configurations is 2 to the power of 10.
• ✊ The formula used to calculate the probability is 10 choose 5 divided by 2 to the power of 10.

Questions & Answers

Q: What is the question posed in the video?

The question asks for the probability of a robot returning to the original position after making 10 random moves.

Q: What is the probability of returning to the original position after 10 moves?

The probability is determined to be 63 over 200, which is approximately 24.6%.

Q: How can the moves be configured to return to the original position?

One possible configuration is to have the first five moves towards the right and the next five moves towards the left. Other configurations are also possible, as long as five moves are towards the right and five moves are towards the left.

Q: What is the formula used to calculate the probability?

The formula used is the number of ways to get five moves towards the right and five moves towards the left divided by the total number of possible configurations, which is 10 choose 5 divided by 2 to the power of 10.

Summary & Key Takeaways

• The video presents a question about the probability of a robot returning to the original position after making 10 random moves.

• The answer to the question is determined to be 63 over 200, approximately 24.6%.

• The video explains the different configurations of moves that can result in returning to the original position and discusses the total number of possible configurations.