Lessons in Probability

I was very fortunate in getting my hands on some free tickets to see Assistant Thief last night. It's a very funny show, one that's worth the $1K or so that tickets cost.

On getting to Centerstage, G and I were handed what appeared to be advertisement handouts. The lady that issued them told us that there were forms on the back to fill out and submit for a chance to win a prize on the night, or a grand prize to be drawn at a later date. When we got in, we found out that the nightly prize was a $500 overseas calling card...

During intermission, a young lady walked to the front, got everybody's attention, and asked a little boy to help do the draw. Now, the theatre holds about 300 people, but not everybody would have filled out their form. Let's assume that 100 people did (I'm sure it was more). Then the probability of anyone being picked from the box was 0.01 [you know, 1÷100 :-) ]. That lucky person was a woman in about row 5. She quietly identified herself and claimed her prize.

After the draw,a gentleman jumps up, displays a basket of goods and informs us that a second draw will be done. This draw was done using the tickets rather than the forms, and thus would have amounted to about 300 in total. Probability of being selected- 0.003. The ticket number was called, and Ms. 0.01 jumped out of her seat. The audience jeered, but she wasn't joking. She had the winning ticket, again.

They jeered. I laughed. This event was so ridiculous, it was funny. The probability of that one lady winning twice is the product of both probabilities, 0.01 and 0.003- that is, 0.00003, or 3 in 100,000. Now that is ridiculous.

I sat there thinking to myself, "Probability is such a sham!" Have you ever tried throwning an orange seed through a grill, and marvel at the fact that despite the large spaces between the grills the seed always seems to hit the grill? Well last night that was the feeling... times 1000. But I thought about, and realized that we as humans have a knack for noticing the things that shouldn't happen instead of appreciating the things that should and do happen. We never remember when that seed goes through the grill, but the second it hits it, we're all over it.

That's what happened last night. Many shows have taken place with many people putting tickets in boxes and having a draw done. However not many people on earth have witnessed what I did last night. And that's the reality of it- what happened last night, odd as it was, was not a regular occurrence, and that's exactly what probability teaches. Probability doesn't necessarily say that something can't happen, but that the chances of it happening are one in a million, or, in this case, 3 in 100,000.

Anything is possible.