Birthday “Paradox” There are N people in a room.

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Presentation transcript:

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

Match Probabilities Pick numbers at random (0..9) Choose a number (0..9) Now pick a number at random, what is the probability of getting the chosen number? Pick numbers at random (0..9) What is the probability that you get two numbers with same value? 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 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

n p(n) 10 12% 20 41% 30 70% 50 97% 100 99.99996% 366 100%