26) In a class of 30 students, approximately what is the probability that two of the students have their birthday on the same day (defined by same day and month) (assuming it's not a leap year) ? For example - Students with birthday 3rd Jan 1993 and 3rd Jan 1994 would be a favorable event.

Question

Mathematics

Makhi Chandler

25 February, 21:29

26) In a class of 30 students, approximately what is the probability that two of the students have their birthday on the same day (defined by same day and month) (assuming it's not a leap year) ? For example - Students with birthday 3rd Jan 1993 and 3rd Jan 1994 would be a favorable event.

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Answers (1)

Know the Answer?

Tate Blair · Answer 1

Answer is 0.696

Step-by-step explanation:

The sum number of sets possible for no two students to have the same birthday in a class of 30 is:

=30 * (30-1) / 2

= 435.

Now, there are 365 days in a year. Therefore, the probability of students having a birthday on a different date would be 364/365. Now there are a number of combination, to be exact 870 combinations.

So, the probability that no two students having the same birthday is:

(364/365) ^435 = 0.303.

Now, the probability that two students would have their birthdays on the same equal date would be:

1-0.303 = 0.696 or 70%