Real-Life Scenarios
Text Version

(Introduction music)
Image description:  Andrew and Khalid are standing outside of the duck pond game booth at the community fair. Justyce is behind the booth, and Marissa walks over to the boys.

Khalid: Okay, so to win a small prize, you need to choose a duck with a prime number, given that you choose an odd-numbered duck.

Image description: As Khalid speaks a close-up of the rules for winning a prize is shown. Written on the rules board is "Win a Small Prize: Choose a duck with a prime number, given that you choose an odd-numbered duck!"

Marissa: That isn’t what Andrew said. He said that to win a small prize, you just have to get a prime number.

Khalid: What is the difference? Isn’t the probability of getting a prime number the same as the probability of getting a prime number given that you get an odd number?

Andrew: Let me explain by first listing out the prime numbers from 1 to 30: 2, 3, 5, 7, 11, 12,17,19,23 and 29.

Image description: As Andrew lists the prime numbers on his clipboard, the numbers appear on screen.

Andrew: There are ten prime numbers. If we just have the prize awarded for pulling a duck with a prime number, this would be ten-thirtieths or one-third.

Image description: Ten-thirtieths or one-third appears on the screen.

 Andrew: Now, I’ll list the odd numbers from 1 to 30: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27 and 29.

Image description: As Andrew lists the odd numbers on his clipboard, the numbers appear on screen.

Andrew: Recall the probability of getting an odd number is fifteen-thirtieths or one-half.

Image description: Fifteen-thirtieths or one-half appears on the screen.

Andrew: I’ll highlight the prime numbers in the list.

Image description: Andrew uses a highlighter marker to highlight the numbers that he wrote on his clipboard: 3, 5, 7, 11, 13, 17, 19, 23 and 29.

Andrew: The probability of selecting a duck that displays a prime number from the ducks that display odd numbers is nine-fifteenths, which simplifies to three-fifths.

Image description: As Andrew speaks, nine-fifteenths and three-fifths appear on screen.

Khalid: The probability of selecting a duck that displays an odd number is one-half. The probability of just selecting a duck that displays a prime number is one-third. However, the probability of choosing a duck which displays a prime number given that you drew a duck that displayed an odd number to begin with is three-fifths.