How many people do you need in a room before any two are more likely than not to have the same birthday?


I’m sure there are those who disbelieve, saying “I know that can’t be right.”  What is disturbing is that even when a simple proof is delivered, many continue not to believe it.  That is stupid, but these days disbelief of reality by people in power is beginning to destroy this country.  The proof looks at the probability that two people don’t have the same birthday.   Here are the probabilities:


Number of People Prob (2 have same Bday) Probability (2 don’t)
2 0.003 0.997
5 0.027 0.973
10 0.117 0.883
15 0.253 0.747
20 0.411 0.589
22 0.476 0.524
23 0.507 0.493
25 0.569 0.431
30 0.706 0.294
35 0.814 0.196


A disease has a prevalence of 1 in 200 (0.5%), a sensitivity of 98% and specificity of 99%, meaning if you have the disease you test positive 98% of the time and if you don’t you test negative 99% of the time.  Not knowing if you have the disease, you test positive.  What is the probability you will have the disease?   The issue here is that having the disease and testing positive is very different from testing positive and wondering if one has the disease.  If the disease is rare, the likelihood of a positive test’s being a false positive is significant.  Here’s why, using 10,000 people and the above percentages:


  Test Positive Test Negative Total
Disease Positive 49 1 50
Disease Negative 99 9851 9950
Total 148 9852 10000


If you test positive (148), a third of the time (49) you will have the disease.  The others are false positives.  That’s why we don’t do routine HIV blood tests for marriage.  In a randomly selected individual, and that is important, a positive test for something rare has a significant likelihood of being a false positive.

Many mountaineers defend the safety of their sport by saying one can get killed in a car accident.   We all know someone who died in a motor vehicle accident, but relative to the denominator, it is small, 1 in about 7000 Americans each year.  Mountaineering is a small community, and number of climbs is a small denominator.  Every serious mountaineer has lost several friends in the mountains.  Mountaineering is far more dangerous.

The lottery is a tax on those who don’t understand probability.  The chances of winning the Powerball jackpot are approximately those of randomly picking a minute chosen since the Declaration of Independence was signed, 1 to 110 million.  Yet people continue to tax themselves because “if you don’t play, you can’t win.”

Too many Americans play “I’m sick do I see a doctor?” lottery:  I have abdominal pain, and I don’t have insurance. I hope it goes away.  But it doesn’t; instead, the pain worsens.  I call an ambulance, go to an ED and am admitted with a ruptured appendix.  The costs have increased and are well in five figures.  I’m bankrupted by the illness, nobody gets paid, and my productivity is zero for a long time.  I’ll probably never get out of debt.  If I get sick again, I’ll bet again it goes away.  I will have no other choice. I’m betting that my body’s natural healing ability will bail me out.  Maybe it will.  Or maybe it won’t.

We were once the richest country in the world.  Our annual medical costs are far more than a trillion dollars.  A trillion is roughly the number of days since the Earth formed.  How many these costs could have been avoided by timely prevention?  How many could have been avoided by universal coverage?  I don’t know.  But I do know that our system makes it impossible for at least a sixth of Americans, not Zimbabweans, to get decent, timely care and not be bankrupted by it.  If you don’t want my solution, you fix it.   Here are my metrics:  your fix has to show an increase in productivity, a decrease in emergency department overcrowding, a decrease in bankruptcies that are primarily due to medical reasons and a decrease in late diagnosis of disorders like appendicitis, that should all be picked up early–in America, not Tajikistan.

If that requires I pay more taxes, I’ll pay them.  I’d rather pay taxes for education and health care than for fighting,  foreign aid to countries who despise us and bailouts to car makers who built monstrous SUVs, when it was obvious decades ago we needed to retool.  The selfish say, “I got mine, and the hell with you.”  Liberals like me say, “I got mine, and I want to help you get yours.”

I’m a patient, and I’m tired of waiting weeks to see a physician (I thought only Canadians waited), worrying about medical errors that affected me and three family members and really tired of the bickering and the lies that stalled any meaningful reform.  It is disgusting and un-American.

The above birthday problem was solved by looking at what we didn’t want to find what we did want.  I don’t want a huge national debt.  Here are 2 thoughts:  end our wars, and enact a 90% marginal tax rate on those with incomes over $3 million.

I can live with 70%.


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