TED-Ed: Check your intuition: The birthday problem - David Knuffke

The video explores the birthday problem, which shows that in a group of 23 people, there's a 50.73% chance that two people share the same birthday. This counterintuitive result is explained using combinatorics, focusing on calculating the probability of no shared birthdays and then subtracting from 100%. The video highlights the rapid growth of possible pairs as group size increases, making shared birthdays more likely. It concludes with real-world examples, illustrating how math can reveal unexpected probabilities.

What is the probability that two people in a group of 23 share the same birthday?

• 50.73%

• 99.9%

• 23%

• 75%

Which mathematical field is used to solve the birthday paradox?

• Algebra

• Calculus

• Geometry

• Combinatorics

How do you calculate the probability of no shared birthdays in a group?

• By multiplying the probabilities of different birthdays

• By dividing the probability of shared birthdays by the number of people

• By subtracting the probability of shared birthdays from 100%

• By adding the probabilities of shared birthdays

How many possible pairs are there in a group of 23 people?

• 115

• 253

• 365

• 46

What happens to the number of possible pairs as the group size increases?

• It decreases linearly

• It remains constant

• It grows quadratically

• It decreases exponentially

In a group of 70 people, what is the probability that two people share a birthday?

• 75%

• 50%

• 23%

• 99.9%

What does the birthday paradox illustrate about coincidences?

• They are impossible to predict

• They are often less coincidental than they seem

• They are always unlikely

• They are always purely random