Should You Be Afraid Of Sharks? Probability and Probabilistic Thinking
This is part 3 of a series of posts about things that should be in math curricula. This post isn’t about a specific topic, but rather about how probability is taught in K-12 curricula.
Many people are scared of sharks. They are prehistoric killing machines, with rows of sharp teeth made for tearing apart flesh.
Having said that, should we be afraid of sharks?
If you posed this question, in the exact same words, to your students, what would they do? This could lead to a probabilistic inquiry, in the very purest sense of “inquiry”: finding information and facts to justify an opinion, in this case, using the tools of mathematics, and our own reasoning abilities.
Not if you never go in a ocean. Jaws doesn’t come out of the water (except for the rubber Jaws on a track they used in a movie). If you never go in the ocean, your probability of being attacked by a shark (except, also, I suppose, for a LandShark), is zero.
Should you be afraid of sharks?
Many years, there are around 65 shark attacks in the entire world, distributed over all the swimmers, surfers, and boaters of the world.
You decide whether 65 shark attacks (many of which are not fatal) are enough to dissuade you from swimming in the ocean, when those 65 shark attacks are distributed over millions of instances of swimming, surfing, and boating.
Sharks are finely tuned killing machines, with teeth that can tear your flesh to shreds.
Should you fear or respect sharks? If you do decide to swim in the ocean, how do you manage the risk of shark attack?
- forget about sharks (“It won’t happen to me.”)
- don’t swim with open wounds on your body.
- avoid New Smyrna Beach, Florida (apparently the most common place in the world, where sharks attack).
- don’t swim at beaches where shark attacks have frequently happened (of course, events tend to happen in clusters, so 3 shark attacks in 2 years at one beach should mean that maybe you DO swim at that beach, unless their favourite prey also lives in the ocean at that beach).
Knowing what it makes sense to be afraid of, and managing risks, is probabilistic thinking. Schools are pretty decent at teaching probability (at least, in that technical way we teach most math subjects). Students learn about games, dice, cards, and various other events, but curricula doesn’t often address one of the key benefits of probabilistic thinking:
managing risk in our lives, and knowing when to act, and not to act.
Here are some things you are more likely, statistically, to die from, than shark attacks:
fireworks lightning, drowning, car accidents, strokes, or heart disease.
Now to change the question we proceeded from:
should you be afraid of fireworks?
Not if you’re not too close to them, as they are being fired.
Should you be afraid of lightning?
Not if you are not waving golf clubs in thunderstorms, or standing under large trees with large limbs that can fall on you.
Should we be afraid of drowning?
Definitely. “Fear death by water”: T.S. Eliot. That’s why it’s important to learn how to swim-to mitigate the risk of drowning.
Should be be afraid to drive in cars?
Definitely. Piloting a one tonne hunk of steel and plastic down a highway should give everyone a slight fear. However, cars are safer than ever before, and self-driving cars will likely help, as their AI improves.
Driving in cars is a risky thing we do on many days of our lives. We manage that risk, by not driving too aggressively or fast, and wearing seat belts.
Should you be afraid of your own heart?
There are ways to manage this risk, not eating too many bacon double cheeseburgers, for one thing, and exercising, for another.
All probabilities are conditional, not absolute. Perhaps there are places in the world’s oceans where the probability of shark attacks is zero. Perhaps we can assign the risk of being attacked by a shark a number somewhere between zero, and whatever the probability of being attacked at New Smyrna beach is.
On average, the Internet says that the odds of being attacked by a shark are something like 1 in 4 000 000, or even 1 in 11 000 000. These are around the odds of certain lotteries, and we don’t assume that we will win those.
Then again, lotteries might be the opposite case: we gamble because we hold out that hope, however faint, that we will be “the one”.
We treat lotteries and sharks very differently, with hope and fear, respectively. Both outcomes have a near zero probability, going by the numbers.
Lotto 649, here in Ontario, apparently gives you a 1 in 14 000 000 chance to become a millionaire. My friend, I can confidently say that it will not be YOU.
(Then again, some people win the lottery, and some people are bit by sharks…)
Why be afraid of near zero probabilities, and why hope for them, for that matter?
Here is the percent for the lower value for chances of being attacked by a shark:
Feel better now?
Now for Lotto 649:
Happy now? You are more likely to be attacked by a shark. Now put that $2 back in your pocket. You’d be better off buying a cup of coffee with it.