8. Thinking, Inquiry, Problem Solving There are 25 students in a Data

Management class. Determine the probability that at least two of them

share the same birthday. (Assume that every year has 365 days.)

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## conditional probability

this question requires conditional probability

i.e. probability of A = 1 - probability of B

so we have 25 people.

therefore the first persons birthday is 1/365.

the probability that the next person does not have the same birthday is 364/365.

third is 363/365.

fourth is 362/365.

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so when we get to the 25th person, the probability that the birthdays are different is:

364/365 * 363/365 * 362/365 * ... * 341/365.

therefore the probability that one person has the same birthday as the other in 1 - this answer.

= 1 - 0.431300296

= 0.568699703

which is approximately 57%.