# math, help

I need help or hint on the setup:

what is the probability that at least 2 students in a class of 36 have the same birthday?

This is 1 minus the probability that all students have different birthdays. Suppose that the birthday of a student is completely random. Then we can evaluate the probability by counting in how many ways we can assign different birthdays to the 36 students and divide that by the total number of ways a birthday can be assigned to a student.

Clearly, the number of ways you can assign different birthdays to the students is:

365!/(365-36)!

This is:

365*364*...*330

For the first student you are assigning a birthday to, you have 365 choices, for the second there are 364 choices left, etc.

The total number of ways bithdays can be assigned is, of course:

365^36

The probability that all students have different birthdays is thus:

365!/[(365-36)! 365^36]

The probaility that this is not the case is therefore:

1 - 365!/[(365-36)! 365^36]

If it is not the case that all students have different birthdays then at least two students must have the same birthday, so this is the desired probability.

You can use Stirling's formula to numerically evaluate the expression:

Log(N!) = N Log (N) - N
+ 1/2 Log(2 pi N) + 1/(12 N) + ...

Log(365!) = 1792.3316

Log(329!) = 1581.7202

36 Log(365) = 212.3963

And therefore:

365!/[(365-36)! 365^36] =

Exp[1803.9383 - 1581.7202 - 212.3963] =

Exp[-1.7849] = 0.16781

1 - 0.16781 = 0.83219

1. 👍
2. 👎
3. 👁

## Similar Questions

1. ### Math

A number cube is rolled 100 times. The results are shown in the table below. Outcome: 1, 2, 3, 4, 5, 6. Number of times rolled: 22, 18, 9, 11, 19, 21. Find the experimental probability and express it as a percent. P(even) = ? A.

2. ### statistics

The below table shows the probabilities generated by rolling one die 50 times and noting the up face. What is the probability of getting an odd up face? roll 1 Probability 0.22 roll2 probability 0.10 roll 3 probability 0.18 roll 4

3. ### physics

To measure the static friction coefficient between a 1.6-kg block and a vertical wall, the setup shown in the drawing is used. A spring (spring constant = 400 N/m) is attached to the block. Someone pushes on the end of the spring

4. ### Solar Energy Help ASAP

John has used a solar simulator setup to measure the relation between the voltage and the current of a small photovoltaic cell (40 cm long and 40 cm wide). The measurement setup maintains the standard measurement conditions: the

1. ### Math

The table below shows the results of flipping two coins. how does the experimental probability of getting at least one tails compare to the theoretical probability of getting at least one tails Outcome: HH HT TH TT # of times

2. ### math , probability

Let X and Y be two independent and identically distributed random variables that take only positive integer values. Their PMF is px (n) = py (n) = 2^-n for every n e N, where N is the set of positive integers. 1. Fix at E N. Find

3. ### Chemistry

You have a chemical sealed in a glass container filled with air. The glass container has a mass of 200.0 grams and the chemical has a mass of 850 grams. The total mass of the setup is 1050 grams. The chemical is ignited by means

4. ### math

A six-sided, fair number cube is rolled 100 times as part of an experiment. The frequency of the roll of the number 3 is 20. Which statement about rolling a 3 is correct? The theoretical probability is 1/6. The experimental

1. ### Physics Lab

(a) For the rotating mass in the lab setup by what ratio will the velocity change if the period is quadrupled? (b) For the rotating mass in the lab setup by what ratio will the velocity change if the period is decreased by a