Probabilities and Coincidence of Shared Birthdays Use a

Chapter 11, Problem 73

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Probabilities and Coincidence of Shared Birthdays

Use a calculator to solve this exercise. Round probabilities to three decimal places.

a. If two people are selected at random, the probability that they do not have the same birthday (day and month) is \(\frac{365}{365} \cdot \frac{364}{365}\). Explain why this is so. (Ignore leap years and assume 365 days in a year.)

b. If three people are selected at random, find the probability that they all have different birthdays.

c. If three people are selected at random, find the probability that at least two of them have the same birthday.

d. If 20 people are selected at random, find the probability that at least 2 of them have the same birthday.

e. Show that if 23 people are selected at random, the probability that at least 2 of them have the same birthday is greater than \(\frac{1}{2}\).

Text Transcription:

frac 365 365 dot frac 364 365

frac 1 2