Archives for probability



What Are the Odds of Twins Born in Different Years?

The following is a guest post by Louise Firth Campbell and Amram Shapiro, the authors (with Rosalind Wright) of The Book of Odds: From Lightning Strikes to Love at First Sight, the Odds of Everyday Life.

Rare news stories recur with surprising regularity — one of these annual stories is the birth of twins in two different years. 

You can see the appeal to editors. Babies are photogenic, especially twins. The symbolism of the New Year as a baby which ages to dotage by year end is an old one, a staple of thousands of New Year’s cards. There is an interesting apparent time tension in the story. Twins share a womb and genomes. Yet a few seconds separation in time of birth makes an apparent year’s worth of difference.[1]  This event is considered a rarity and only a handful of cases are reported in the press each year. This rarity makes it news, but is the event really as rare as it seems?

Let’s start with the news in 2013/2014. If the cases reported in the North American media, two in the U.S. and one in Canada, are the only cases, these events are rare indeed. There are about 4 million births a year in the U.S. That would suggest these events are as rare as 1 in 2 million. Someone visiting the Grand Canyon is more likely to die by falling off the edge (1 in 1.5 million).[2]  That doesn’t feel right to us. Read More »



Classrooms With 500,000 Students

I am fascinated by the Stanford online courses in machine learning and artificial intelligence. My first inkling of them came when quite a few of my students started taking the artificial-intelligence class. Olin is very small, only about 400 students, so I realized that these online courses must be large. But I almost fell over when I saw that enrollment varied from 66,000, at the low-end, to 160,000.

Sebastian Thrun, who co-taught the artificial-intelligence course to 160,000 students, is now leaving Stanford teaching in order to teach courses to 500,000 students for free. What an inspiring goal! Read More »



Probabalistic Auctions: Why Don’t Universities Raffle off Chair Endowments?

A recent post of mine was addressed to the super-rich who are considering endowing a chair in order to garner public recognition. But what about the merely rich who wish to have their names recognized in perpetuity with an eponymous endowed chair at their university? Is there anything they can do?

Yes. There are two things.

First, a much larger swath of people can follow the Benjamin Franklin strategy and endow a delayed chair. Franklin famously bequeathed about $4,000 in 1790 to the Commonwealth of Pennsylvania. Franklin:

instructed that [his bequest] be invested for two hundred years and at the end of that period, the money should be used to do good. Franklin died in 1790. In 1990, his gift had grown to over $2 million.

Read More »



Answer to Same-City NCAA Sweet 16 Questions

Last week, we posed two questions regarding the NCAA basketball tournament: what are the odds that two teams from the same city would make the Sweet 16? And when was the last time that happened? To the first person to answer correctly, we offered some Freakonomics swag. And you responded, 147 of you to be exact. Read More »



A Freakonomics Contest: Odds of Same City Teams in NCAA Sweet 16

Two teams from the same city have made it to the Sweet 16, the University of RIchmond and VCU, both from Richmond, VA. What, we wonder, are the odds of that happening? Read More »



The Odds of Surviving a Plane Crash

The Book of Odds takes a look at a question that flashes through the minds of many people the moment they board an airplane: what are your odds of surviving a plane crash? They found that “[t]he general survival rate for a casualty-inducing airline incident is about 38% or, in our parlance: your odds of survival are about 1 in 2.63.” Read More »



Rebound Rates

The Celtics’ demolition of the Lakers reminds me that the sport announcers would do well to put more emphasis on “rebound rates.” Like putt probabilities, the rebound rate basically tells you the probability that a team will get the next rebound. Can you answer a fairly simple question: In the NBA if a team misses […] Read More »



Putt Probabilities

Like many others, I was incredibly jazzed by Tiger’s victory on Monday. But I was frustrated that the commentators routinely failed to mention the putting distance to the hole. It would be nice to know, “It looks like Rocco has a 25-foot putt.” But I, for one, would like commentators to go further and routinely […] Read More »