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Mathematics & Reason. How understanding maths and reason changes your view of the World. What is Mathematics?. The search for pattern. Betrand Russell. “Mathematics, rightly viewed, possesses not only truth, but supreme beauty.”. Monty Hall Problem. 1. 2. 3. Monty Hall Problem. 1.
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Mathematics & Reason How understanding maths and reason changes your view of the World.
What is Mathematics? The search for pattern.
Betrand Russell “Mathematics, rightly viewed, possesses not only truth, but supreme beauty.”
Monty Hall Problem 1 2 3
Bayes’s Theorem A patient goes to see a doctor. The doctor performs a test with 99 percent reliability--that is, 99 percent of people who are sick test positive and 99 percent of the healthy people test negative. The doctor knows that only 1 percent of the people in the country are sick. Now the question is: if the patient tests positive, what are the chances the patient is sick?
Bayes’s Theorem 99 100 1 99 9900 9801
Penney Ante Game Mathematics in Gambling
Penney Ante Rules 1. You pick a 3-coin sequence (e.g. H T H) 2. I pick a 3 coin sequence (e.g. T T H) 3. We toss a coin repeatedly 4. Whoever’s sequence appears first wins. T H H H H T Hyou win
H H H T T T H H T T T H H T H T H T H T T T H H
Penny Ante is a scam ! Imagine you choose H H H . Eventually we get the firstappearance of H H H : . . . . . . . . . . . ? H H H
Was OJ Simpson Guilty? Mathematics & Statistics in the Courtroom
O.J. Simpson abused his wife and she was murdered. 1 in 1,000 abused women are killed by their husbands. But 80% of murdered abused women are killed by the husbands.
3 Dice… which one would you choose? 3 2 1 3 2 4 3 2 4 3 5 4 3 5 4 6 5 4
3 2 3 2 3 2 vs 3 5 3 5 6 5 BLUE beats GREENon average
2 1 2 4 2 4 vs 5 4 5 4 5 4 GREEN beats REDon average
? 3 2 1 3 2 4 3 2 4 3 5 4 3 5 4 6 5 4
3 1 3 4 3 4 vs 3 4 3 4 6 4 RED beats BLUE!!
625 Two blues beat two reds 671
Benford’s Law • Take a list of data. • Examine how many of the numbers start with a 1, 2, 3, etc
