Fifty people are selected at random. What is the probability that none of the people in this gro

step 1 Our question is, what is the probability date in a group of 20 people that includes no twins at

Fifty people are selected at random. What is the probability...

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Key Concepts

Birthday Paradox

The birthday paradox refers to the counterintuitive probability result that in a relatively small group of people, the chance of at least two individuals sharing the same birthday is surprisingly high. It highlights how quickly the probability builds up as the number of individuals increases, despite there being a large number of possible birthdays.

Independent Events and Uniform Distribution

This concept assumes that each person's birthday is independent of the others and that each day of the year is equally likely to be a birthday. Such an assumption simplifies the calculation by allowing the use of basic probability rules, even though in reality there may be slight variations in birthday distributions.

Multiplicative Principle of Probability

This principle states that the probability of a series of independent events all occurring is the product of the probabilities of each individual event. In the context of the birthday problem, it is used to compute the probability that each subsequent person has a birthday different from those already considered by multiplying successive fractions that represent the remaining available birthdays.

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