1

Birthday “Paradox”

There are N people in a room.

What is the probability that two people have the same birthday?

num = 1.25 sqrt(N)

N=365, sqrt(N) = 19.1

2

Match Probabilities

Choose a number (0..9)

Now pick a number at random, what is the probability of getting the chosen number?

Try Fail Success

1 0.90 0.1

2 0.81 0.19

3 0.73 0.27

4 0.66 0.34

5 0.59 0.41

6 0.53 0.47

7 0.48 0.52

8 0.43 0.57

9 0.39 0.61

10 0.35 0.65

Pick numbers at random (0..9)

What is the probability that you get two numbers with same value?

Try Fail Success

2 0.9000 0.1000

3 0.7200 0.2800

4 0.5040 0.4960

5 0.3024 0.6976

6 0.1512 0.8488

7 0.0605 0.9395

8 0.0181 0.9819

9 0.0036 0.9964

10 0.0004 0.9996

11 0.0000 1.0000

3

n p(n)

10 12%

20 41%

30 70%

50 97%

100 99.99996%

366 100%