Duplicate birthdays There are 30 students in Austin’s precalculus class, all unrelated. He wants to bet you $1 that at least 2 of the students were born on the same day of the year (same month and day but not necessarily the same year). Should you take the bet? Before you answer, you decide to conduct a simulation to see how likely that event would be. Here is the probability model:

Th e birth date of a randomly chosen person is equally likely to be any of the 365 dates of the year (ignoring February 29).

Th e birth dates of diff erent people in the room are independent.

(a) Describe how you could use either Table B or your calculator to simulate 30 random birthdays from the 365 possible days.

(b) Carry out your simulation. Perform 10 repetitions. Based on your results, should you take Austin’s bet?

(c) Combine your results with those from other members of the class. Are you surprised?