5.117 Simulating matching birthdays Do you find it hard to believe that the probability of at least one birthday match in a class of 25 students is 0.57? Let’s simulate the answer.

Using the Random Numbers web app accessible from the book’s website, each student in the class should simulate 25 numbers between 1 and 365. Observe whether there is at least one match of two numbers out of the 25 simulated numbers.

a. Combine class results. What proportion of the simulations had at least one birthday match?

b. Repeat part a for a birthday match in a class of 50 students. Again, combine class results. What is the simulated probability of at least one match?