This exercise is on probabilities and coincidence of shared birthdays. Complete parts (a) through (e) below. a. If two people are selected at random, the probability that they do not have the same birthday (day and month) is 365 364 365 365 Explain why this is so. (Ignore leap years and assume 365 days in a year.) The first person can have any birthday, so they can have a birthday on 365 of the 365 days. In order for the second person to not have the same birthday they must have one of the 364 remaining birthdays. (Type whole numbers.) b. If three people are selected at random, find the probability that they all have different birthdays. The probability that they all have different birthdays is 0.992 (Round to three decimal places as needed.) c. If three people are selected at random, find the probability that at least two of them have the same birthday. The probability that at least two of them have the same birthday is 0.008. (Round to three decimal places as needed.) d. If 14 people are selected at random, find the probability that at least 2 of them have the same birthday. The probability that at least two of them have the same birthday is ☐ (Round to three decimal places as needed.)
This exercise is on probabilities and coincidence of shared birthdays. Complete parts (a) through (e) below. a. If two people are selected at random, the probability that they do not have the same birthday (day and month) is 365 364 365 365 Explain why this is so. (Ignore leap years and assume 365 days in a year.) The first person can have any birthday, so they can have a birthday on 365 of the 365 days. In order for the second person to not have the same birthday they must have one of the 364 remaining birthdays. (Type whole numbers.) b. If three people are selected at random, find the probability that they all have different birthdays. The probability that they all have different birthdays is 0.992 (Round to three decimal places as needed.) c. If three people are selected at random, find the probability that at least two of them have the same birthday. The probability that at least two of them have the same birthday is 0.008. (Round to three decimal places as needed.) d. If 14 people are selected at random, find the probability that at least 2 of them have the same birthday. The probability that at least two of them have the same birthday is ☐ (Round to three decimal places as needed.)
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 39E: Smokers md Nonsmokers The participants at a mathematics conference are housed dormitory-style, five...
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Transcribed Image Text:This exercise is on probabilities and coincidence of shared birthdays. Complete parts (a) through (e) below.
a. If two people are selected at random, the probability that they do not have the same birthday (day and month) is
365 364
365 365
Explain why this is so. (Ignore leap years and assume 365 days in a year.)
The first person can have any birthday, so they can have a birthday on 365 of the 365 days. In order for the second person to not have the same birthday they must have one of the 364 remaining birthdays.
(Type whole numbers.)
b. If three people are selected at random, find the probability that they all have different birthdays.
The probability that they all have different birthdays is 0.992
(Round to three decimal places as needed.)
c. If three people are selected at random, find the probability that at least two of them have the same birthday.
The probability that at least two of them have the same birthday is 0.008.
(Round to three decimal places as needed.)
d. If 14 people are selected at random, find the probability that at least 2 of them have the same birthday.
The probability that at least two of them have the same birthday is ☐
(Round to three decimal places as needed.)
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