There were 42 different presidents of the United States from...

Name: Problem 44, Chapter 8: Applied Mathematics: For the Managerial, Life, and Social Sciences
Uploaded: 2023-09-30T17:43:57-08:00
Duration: 2 min 10 s
Channel: Sanchit Jain
Description: There were 42 different presidents of the United States from 1789 through 2000 . What is the probability that at least two of them had the same birthday? Compare your calculation with the facts by checking an almanac or some other source.

There were 42 different presidents of the United States from 1789 through 2000 . What is the probability that at least two of them had the same birthday? Compare your calculation with the facts by checking an almanac or some other source.

Key Concepts

Uniform Distribution Assumption

The uniform distribution assumption implies that each possible birthday is equally likely for any person, and the events of individuals having certain birthdays are independent of one another. This simplifies the calculations in problems such as the birthday paradox, although in real-world scenarios some birthdays might be more common than others.

Birthday Paradox

The birthday paradox is a counterintuitive result in probability theory which shows that in a relatively small group of people, the probability that at least two individuals share the same birthday is surprisingly high. It demonstrates that as the group size increases, the likelihood of a birthday match grows rapidly, even though the number of possible birthdays (typically 365) is much larger than the number of people in the group.

Complement Rule

The complement rule in probability is a strategy used to calculate the probability of an event by subtracting the probability of its complement from one. In problems like the birthday paradox, it is often easier to compute the probability that no one shares a birthday and then subtract that value from one to find the probability that at least two people do share a birthday.

Probability Calculation Techniques

Probability calculation techniques involve methods such as the use of factorials, permutations, and combinations to determine the number of ways an event can occur. In the context of the birthday paradox, these methods are used to calculate the probability that all individuals have distinct birthdays, which is then used in conjunction with the complement rule to determine the probability of at least one match.

Transcript

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