1. The Birthday Problem Section 6.2.3

2. The Birthday Problem What is the probability that in a group of 37 students at least two of them share a birthday? –Write down your best guess now on a small piece of paper. Give it to me. Do a simulation to answer this question. –As practice for our upcoming test, write out the 5 steps of this simulation as you do the problem. –Run the simulation 5 times and prepare to report to me how many successes you had. –We will combine class results to estimate the probability.

3. 5 Steps of the Simulation 1.State the problem –Estimate the probability that in a group of 37 students at least two of them share a birthday 2.State the assumptions –Each date is equally likely (Use 365 days) –Birthdays are independent (So no twins, etc.) 3.Assign integers –Let the numbers 1 – 365 represent each day of the year, so 1 = Jan 1, 2 = Jan 2, etc. 4.Perform the simulation many times Report your results to me now. 5.State the conclusion –“Based on xxx trials, I estimate the probability of at least one shared birthday in a group of 37 people to be xx%”

4. The Birthday Problem in Theory What is the theoretical probability that in a group of 37 students at least two of them share a birthday? –Hint: Recall what we said yesterday about solving “at least” problems. –Further hint: What is the probability that… The first person in the room HAS a birthday AND the second person has a different birthday AND the third person has a birthday different from both of them AND…

5. Homework Solve The Birthday Problem Read pages 336 – 337 Do problems 28 – 32