The Birthday Paradox

The video explains the birthday paradox, which shows that in a group of 23 people, there's a 50% chance that two people share a birthday, and with 75 people, the chance rises to 99.9%. This counterintuitive result is due to the exponential decrease in the probability of unique birthdays as more people are added. The video details the calculations involved and highlights the large number of possible pairings in a group, which increases the likelihood of shared birthdays.

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

• 75%

• 50%

• 99.9%

• 25%

Why is the birthday paradox considered a paradox?

• Because it contradicts our intuitive understanding of probability

• Because it involves complex calculations

• Because it is based on incorrect assumptions

• Because it only applies to large groups

How do we calculate the probability of shared birthdays in a group?

• By assuming each person has a unique birthday

• By using the average number of birthdays

• By dividing the number of people by 365

• By calculating the probability of no shared birthdays

What is the probability that at least two people share a birthday in a group of 75 people?

• 50%

• 100%

• 75%

• 99.9%

Why do we have a high probability of shared birthdays in a small group?

• Because of the large number of possible pairings

• Because each person has a unique birthday

• Because the year has fewer days

• Because people are born on the same day

How many possible pairs can be formed in a group of 23 people?

• 500

• 253

• 100

• 365

What is the probability that no two people share a birthday in a group of 23 people?

• 99.9%

• 0.73%

• 50.73%

• 49.27%