The Birthday Paradox

The video explains the birthday paradox, which reveals that in a group of 23 people, there's a more than 50% chance that two people share a birthday. This counterintuitive result is derived from calculating the probability of people not sharing a birthday and multiplying these probabilities for each new person entering the room. The video demonstrates that with 57 people, the probability of shared birthdays exceeds 99%, illustrating the surprising nature of probability in large groups.

What is the initial assumption about the number of people needed in a room to ensure a shared birthday?

• 57 people

• 366 people

• 23 people

• 365 people

How does the probability of avoiding a shared birthday change as more people enter the room?

• It decreases

• It remains the same

• It increases

• It becomes zero

What is the probability that two people in a group of 15 will not share a birthday?

• 99.7%

• 75%

• 50%

• 25%

At what group size does the probability of sharing a birthday exceed 50%?

• 57 people

• 30 people

• 23 people

• 15 people

With 57 people in a room, what is the probability that at least two people share a birthday?

• 50%

• 75%

• 99%

• 100%