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Asked by Praveen Last Modified
Answer To find the probability that two different friends have different birthdays, we can consider the total number of possible combinations of birthdays and the number of combinations where the birthdays are different.
In a non-leap year, there are 365 days. Therefore, the probability that two friends have different birthdays is the complement of the probability that they have the same birthday.
Total number of possible combinations of birthdays: Each friend can have their birthday on any of the 365 days of the year. So, the total number of possible combinations of birthdays for two friends is 365×365365×365.
Number of combinations where the birthdays are different: If one friend has their birthday on a specific day, the other friend can have their birthday on any of the other 364 days of the year. So, the number of combinations where the birthdays are different is 365×364365×364.
Now, let's calculate the probability that two different friends have different birthdays:
Probability=Number of combinations where the birthdays are differentTotal number of possible combinations of birthdays
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