Often, though not always, people have a terrible understanding of what is and is not probable. I should probably state the probability that a randomly chosen person will have a terrible understanding of how probable an occurrence is. But then again, that is layering the probabilities, and will most likely only confuse people further.
Let me give you some examples of what I mean.
I was in a faculty meeting at an institution where I worked. We had a visitor from learning support speaking to us. The incoming students had taken placement exams in writing and mathematics. And this speaker was talking about the results.
“What percentage of the students do you think scored below average on both tests?” the speaker asked.
One of the faculty guessed “Twenty-five percent.” And he was exactly right. Then she went on and on bemoaning this fact, saying we had to better support those students.
I raised my hand and asked, “When you say they scored below average, you mean the national average on these tests or just at our institution?”
“Just at our institution.”
And then I was perplexed. On any set of test scores, the median is the score for which half the students did better and half the students did worse. The average, or the mean, may not be the same as the median, but for most sets of data, they're close to each other. So you would expect about half of the students on one test to score below average.
If there are two tests, making no other assumptions about any connections between the scores on the two tests, you would expect about a quarter of the students to score below average on both tests. Why? Because one quarter is one half times one half.
So 25% was exactly the number one should have expected. Why was our speaker going on and on about how terrible this was? I more or less asked this question and got an unsatisfactory answer. Our speaker didn't understand my objection. The curse of thinking mathematically, I guess. At least when others don't.
There are plenty of other examples in society. We concern ourselves with incredibly improbable things while ignoring probable things that just don't seem as catastrophic to us. Some people insist they must be allowed to have guns in the home for protection against home invasion. It sounds reasonable, home invasions would be terrible. But probabilities don't really bear it out. In fact, the probability of being a victim of a home invasion is much smaller than the probability of a death or injury occurring caused by a gun kept in the home.
Still, sometimes we recognize the improbable for what it is, especially when it is improbable with a positive outcome. These things we call miracles.
We learned about a miracle baby on the Island of Penang in Malaysia.
On December 26, 2004, there was a tsunami, as I'm sure many remember. Penang was one of the places hit by that tsunami. And most of the people on the island had no idea it was coming until the waters hit.
This includes a couple who were working at a beachside restaurant. They had brought their baby with them to work and she was laying out on the beach on a mattress. This was just a tiny baby, not old enough to roll off the mattress or crawl away. I know, this sounds like a tragedy in the making, but it's not. Remember, miracle baby.
Yes, the waters rose and somehow, miraculously lifted the mattress up rather than flinging it for miles. And then, just as miraculously, when the waters withdrew again, they set the mattress back down on the beach. The baby was still there, perhaps jostled a bit, but unharmed. Her parents grabbed her and got away.
I wasn't there, so I can't say how it happened. I was only hearing the tale told now, years later. But this girl is called, by the people of Penang, the Miracle Baby. Every year on December 27th, the local newspaper publishes her picture as a baby and her picture at whatever age she is. They tell how she has grown over the past year and give the readers an account of her life.
What would that be like? This girl is local celebrity, she's famous among the people of Penang. And she has been since before she can remember. She won her fame through an act of nature that she had nothing to do with and has no personal memory of it. Do you think it's great? Or do you think it's tons of pressure? Or is it basically like being anyone else, except once a year newspaper reporters come to question you and get your picture?
I don't know. We should calculate the probabilities of each possible outcome.
Nah, why bother? Most people wouldn't understand it anyway.