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What is the probability that 3 children selected at random would have different birthdays?
Most Upvoted Answer
What is the probability that 3 children selected at random would have ...
Probability of three children having different birthdays
Explanation
Let's assume there are 365 days in a year (not accounting for leap years) and each day is equally likely to be someone's birthday. The probability of two people having the same birthday is:
P(2 people have the same birthday) = 1/365 (since there are 365 possible birthdays)
Using the complement rule, we can find the probability of three people having different birthdays:
P(3 people have different birthdays) = 1 - P(2 people have the same birthday)
Now, let's break down the calculation:
- The probability that the second person doesn't have the same birthday as the first is 364/365.
- The probability that the third person doesn't have the same birthday as either the first or second is 363/365.
So the probability of three people having different birthdays is:
P(3 people have different birthdays) = 1 - (1/365) * (364/365) * (363/365) = 0.9918
Conclusion
Therefore, the probability that 3 children selected at random would have different birthdays is 0.9918 or approximately 99.18%. This means that it is highly likely that three children selected at random will have different birthdays.
Community Answer
What is the probability that 3 children selected at random would have ...
362/365 in normal year
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What is the probability that 3 children selected at random would have different birthdays?
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What is the probability that 3 children selected at random would have different birthdays? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about What is the probability that 3 children selected at random would have different birthdays? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the probability that 3 children selected at random would have different birthdays?.
What is the probability that 3 children selected at random would have different birthdays? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about What is the probability that 3 children selected at random would have different birthdays? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the probability that 3 children selected at random would have different birthdays?.
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