# What is the probability that 4 randomly selected people all have different birthdays? Round the answer to four decimal places

thilina-g | College Teacher | (Level 1) Educator

Posted on

There are 365 out of 365 ways to select the birthday of first person. Therefore the number of ways that we can choose a birthday for second person is 364 out of 365.

Therefore the probability of two persons not having the same birthday is,

`P(2) = 365/365 xx364/365`

For four people,

`P(4) = 365/365 xx 364/365 xx 363/365 xx 362/365`

`P(4) = 0.9836`

Therefore the probability of 4 people having different birthdays is 0.9836
The text passage contains a mathematical question about the probability of 4 randomly selected people all having different birthdays, and it also provides the answer to this question.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# What is the probability that 4 randomly selected people all have different birthdays? Round the answer to four decimal places

thilina-g | College Teacher | (Level 1) Educator

Posted on

There are 365 out of 365 ways to select the birthday of first person. Therefore the number of ways that we can choose a birthday for second person is 364 out of 365.

Therefore the probability of two persons not having the same birthday is,

`P(2) = 365/365 xx364/365`

For four people,

`P(4) = 365/365 xx 364/365 xx 363/365 xx 362/365`

`P(4) = 0.9836`

Therefore the probability of 4 people having different birthdays is 0.9836
user
The text passage contains a mathematical question about the probability of 4 randomly selected people all having different birthdays, and it also provides the answer to this question.

TYPE: SINGLE_QUESTION_WITH_ANSWER