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.  Our minds can play tricks on us.  That’s normal.  But in the face of a compelling proof, failure to accept the premise borders on stupid.  The proof, by the way, looks at the probability that two people don’t have the same birthday.  Sometimes, looking at what you don’t want makes it easier to find what you do want.  Here’s the proof:

Number of People              Probability 2 have same birthday           Probability 2 don’t

1                                                   0.000                                                          1.000

2                                                   0.003                                                          0.997

3                                                   0.008                                                          0.992

5                                                   0.027                                                          0.973

10                                                 0.117                                                           0.883

15                                                 0.253                                                           0.747

20                                                0.411                                                             0.589

21                                                 0.444                                                           0.556

22                                                 0.476                                                           0.524

23                                                 0.507                                                           0.493

25                                                 0.569                                                            0.431

30                                                 0.706                                                           0.294

35                                                 0.814                                                            0.186

A disease has a prevalence of 1 in 200 (0.5%), a sensitivity and specificity each 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 percentates:

Test + Test – 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.  That’s true.  But nearly all of us drive and a lot.  We all know someone who died in a motor vehicle accident, but relative to the denominator, it is small, 1 in about 5000 to 6000 Americans this year.  Mountaineering is a small community, and number of climbs is an incredibly small fraction of number of auto trips.  Every serious mountaineer has lost several friends to the mountains.  Mountaineering is much more dangerous.  I love reading about it, and I admire those who do it, but it is high risk.

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.”  You have far more likelihood of being struck by lightning or dying in a motor vehicle accident than you do winning the lottery.

Too many Americans play another lottery, the I’m sick do I see a doctor? lottery:  I have abdominal pain, and I don’t have insurance.  I can’t afford to see a doctor, so I will bet it goes away.  But it doesn’t; instead, the pain worsens, and I now can’t walk.  I have to call an ambulance, go to an emergency department and am admitted with a ruptured appendix.  The costs have increased and are well in five figures.  I’m bankrupted by the illness, few who are involved in the care get 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.

Well, you say, that is just a bad example.  Here’s another:  I have abdominal pain and go to urgent care, because I don’t have a family doctor or it takes weeks to get in.  The workup costs $2000.  I can’t pay it except in $20 increments.  That was my Literacy Volunteer student’s experience.   How many Americans say some morning “I  have a toothache, I can’t afford to take off work.”  They are miserable, and their productivity isn’t very good.  Maybe it will go away, or maybe they will need a root canal, which hurts like hell, because there is already a problem.  That’s about $1200, so they are more in debt.  Sure, they say. if I had the money for dental care, I might have been able to avoid this.  Instead,  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, by the way, 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 poor system makes it impossible for at least a sixth of Americans to get decent, timely care and not get bankrupted by it.  This is America, not Zimbabwe, India or Tajikistan.  If you don’t like my solution, you fix it.  And not by going back to the 20th or 19th century, since going backwards never works.  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, again, 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, and not building schools in Iraq and Afghanistan, which is the fundamental solution to terrorism, not nuking Muslims and letting Allah sort it out.  We stop 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.

Do I like government as a single payer?  No.  But again, if you disagree, you fix it.  I don’t want reading assignments.  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 have affected me and three family members and really tired of the bickering that has stalled any kind of reform.  It is disgusting – and is un-American.

The America I served used to have innovative solutions to tough problems.  Where is that country?

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