A Little Mathematics Maestro!

Some skeptics will read the last post and laugh at the idea of cold calling as a viable way of locating working vacations.  With images of struggling telemarketers firmly in mind they argue you would need to contact hundreds of institutions to have even the tiniest chance of success.  I want to show you they are wrong, not just by saying it but by proving it mathematically!

A few years ago the New Yorker ran a cartoon entitled “What Hell Is Really Like.”  There was Satan, complete with horns and pitchfork, standing over some poor, unfortunate wretch writhing in pain and straining to read the words on a piece of paper.  It said “A train leaves New York going 40 miles per hour … ”  While I don’t believe that Hell is an endless series of algebra story problems, I know that many of you will smile and sympathize.  Therefore, I tread carefully when presenting a mathematical argument, and I will try my best not to make this too difficult to follow.

Let’s assume there is one chance in twenty (probability p = 0.05) of success, i.e., of getting a “Yes, we want you” response to your cold call or blind email.  That means you will get back a “No thank you” nineteen times out of 20 (p = 0.95).  Furthermore, let’s say you have contacted four institutions, A, B, C, and D, trying to find that dream offer.

The likelihood that exactly one of these four places says Yes is equal to the chance of getting exactly one Yes and exactly three Nos, which mathematically is  equal to (0.05) x (0.95) x (0.95) x (0.95) = 0.0428687 .  However, that single Yes could come from either A, B, C, or D, so the overall probability of getting exactly one Yes from any one of your four inquiries is four times that previous number, or 4 x 0.0428687 = 0.1715.

However, the true odds are better than that.  If you are a lucky individual you might get two Yeses from your four cold calls.  Of course you cannot accept two jobs at the same time, but you are free to pick the one that best suits you. There are six different ways that two places can both say Yes:  (A, B), (A, C), (A, D), (B, C), (B, D), and (C, D).  The chance of any one of these events happening is the probability of getting exactly two Yeses and exactly two Nos, which is (0.05) x (0.05) x (0.95) x (0.95) = 0.0022562.  So, the overall probability of getting exactly two Yeses from anywhere is 6 x 0.0022562 = 0.0135.  I won’t go through the mathematics of exactly three and four Yeses (rare events) but the sum of all these values is the probability that you will receive one or more Yeses in response to your four inquiries. That final total is 0.1855, or about 18.6%.

Now think about what that means. Even if you have only one chance in twenty of anyone being interested in you, simply by contacting four schools you will have improved your chances of landing a position from one in twenty to 18.6%, almost one in five.  If I told you that spending an hour or so on your computer would result in a one in five chance of an all-expenses paid three-month safari to Kenya would you do it?  Of course you would.  Well, then, why haven’t you!

And you can do even better.  As I said in my last post, the Web makes it very easy to get names and addresses of overseas institutions, so why limit yourself to contacting just four?  If, for example, you send out eight emails (assuming there are eight institutions where you could work), and the probability of success is still one in twenty, the odds go up to one chance in three!  With thirteen emails, you will have a 50/50 chance of finding and getting that dream vacation.  Now that doesn’t sound like the impossibility skeptics would have you believe, does it?

And, finally, for those who scoff at my assumption of a one in twenty chance of success (a value based on my own cold calling experiences), let’s lower the chances to one in fifty.  Even with these dismal odds (who would bet on a 50-1 shot at the racetrack?) if you were to send out eight exploratory emails you will have a 15% chance of landing a position; send out fifteen emails and your odds go up to one in four–a heck of a lot better than the lottery!   With the universal availability of the Web, word processors, and free e-mail software, sending out fifteen inquiries is probably not even one afternoon’s labors.

So, for all those individuals who have been able to wade through my mathematical arguments this far, I hope you are now motivated enough to send out a few unsolicited emails to those dream destinations–India, Norway, Germany, Austria–you described in your comments.  Remember, the odds are in your favor!

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