Governor Rick Perry of Texas signed a law on Monday that makes it easier to conceal guns and advocated allowing gun owners to carry guns anywhere they want – schools, churches, could he possibly mean courts as well? — so that the kind of tragedy at Virginia Tech could be avoided. (Yep, he means courthouses as well. Read the link above to the Dallas News.)
I thought at first that this must be a prank when I heard it on NPR. Can any sane individual actually believe that giving everyone a gun — sane, momentarily insane, insane, frequently insane, unpredictable, occasionally nuts — would make such a tragedy less likely or prevent it from happening? Here, it would seem, that birthday probability algorithm might help us see more clearly.
You know this one. In any given room, the number of people who have a birthday on the same day is much higher than we would expect since there are 365 days in the year. So intuitively we’d expect that the probability that someone has the same birthday we do is 1/365 if we ignore leap years, which is a very small probability. So if there are say 23 people in the room, you might expect intuitively that the probability that there are two people with the same birthday to be 23 * (1/365) or about 6%. This, at any rate, is what we feel in our gut. But in fact, the probability that in a room of 23 at least two people will have the same birthday is about 50%.
To get to this correct, non-intuitive answer, you need to consider first the probability that you have the birthday you do. That’s 1. The probability that the next person has a different birthday from you is then 364/365. And the probability that the third person has a different birthday from you and the second person is 363/365. Continuing this on and multiplying out the numbers, the probability that two people in a room of 23 don’t have the same birthday is:
(365/365)*(364/365)* . . . *(342/365) = 0.4927 or ~50%
Since this is the probability that no two people in a room of 23 have the same birthday, the probability that two do have the same birthday is just 1 – .5 or also 50%.
Might we not use the same logic to determine the probability that someone in a room will shoot someone else if everyone is armed? Instead of a birthday, we would need to figure out the probability that a person with a gun, which would now be everyone in the room, would be in a mental state sufficiently angry such that if he came into contact with another sufficiently angry person that a heated exchange would lead to gunfire. Might we not use the same number as the number of days in the year to make the calculation easy?
In other words, let’s assume that there are 365 discreet mental states, one of which is an insane state that would lead to someone feeling as though he wants to kill someone else. If we then ask what the probability is that at least two people are in the same mental state, which would probably precipitate a confrontation, then we have the birthday problem again, where S in the number of mental states and n is the number of people in the room:
1-P(S) = (S!/S**n/(S-n)!)*(1/S)
= S!/S**(n+1)/(S-n)!
We multiply by 1/S since this is the probability that the mental state these two or more people are in is the evil, angry state, capable of leading to a shooting. For the case that there are 365 mental states and 60 people in the same space, for example, close enough to one another to have contact, then the probability that two will be in the same mental state is 99%, virtually certain.
This means that there is then a 1/365 or ~0.27% probability that shots will be fired. While this is a small probability, would you get into a car if this were the probabiliy that you’d be injured or into an airplane if this were the probability the plane would crash? When it’s life threatening, a 1/365 probability is damn high.
In addition, I’ve used 365 mental states when in fact my guess is that there are many fewer mental states, which means that even in a small group, say 20 or 30, the probability that two are in the same mental state is virtually certain. And then if you factor in the kind of mental focusing that takes place when alcohol or drugs are involved at a sporting event or concert, the probability would quickly become large that at least two would be in the same nasty mental state. And if everyone had a gun, the probability would be high that someone would get shot.
Even in the wild wild west, if we’re to believe our Westerns, the sheriff knew better than to let cowboys pack guns when they were in town.
The boat was always under control and on a broad reach we’d get to 9 or 10 knots in twenty knots or more of wind. But when the winds died away, as they always did near Pinole Point or Point Richmond, Fishcake’s velocity made good would vanish and we’d motor.
But last year near the end of the season, yacht broker Gary Helms made it possible for us to trade Fishcake for Dulcinea, a new Corsair Sprint 750, which is a 24-foot foldable trimaran that flies across the water — five knots now seems as though we’re not moving — even in light winds.
Fishcake, for the ride was always high and dry, but somehow we seem to be adjusting to salt spray flying everywhere and 15 knots on a beam reach, 20 knots if we dare deploy our spinnaker in a sock, but we’re not there yet.
went — Â for Shakespearean and other theatre, so the thought of a city of Ashland’s qualities without a library was certainly tragic even though we didn’t go to the library more than a few times. But then we don’t live there: we just visit.
