A friend of mine recently posted on Facebook:

You know in movies, when they wash a spider down the drain and it crawls out from that little overflow hole at the top of the tub? That just happened while the girls were in the bath. Only in real life, it didn’t kill anyone or give them super powers.

She later admitted, in response to disappointment that she had flushed the spider:

Next time I’ll give it a shot at a bite and we’ll find out if I live in a horror movie or a superhero movie. (Or the harrowing tale of two children being taken from their insane mother, who allowed spiders to bite them in hopes of super powers for them.)

and

Super powers are more likely than poison anyway, right?

It was at this point I felt compelled to chime in. Being someone with a “mild superpower” I am uniquely qualified to answer this question.

It’s 50/50. Either it happens or it doesn’t. Two possibilities, one outcome. Basic statistics.

In fact, I had answered a similar question years before on a poker forum, so the heavy lifting had already been done.

A member asked:

What are the odds…of losing 3 SnGs in a row to your opponent making a full house on the river when you get it in with a flopped straight, flopped trips, and top two pair.

I replied:

50%

either it happens or it doesn’t.

2 possibilities, 1 actual outcome.

1/2 = .5 or 50%

coincidentally that’s the same probability of it raining tomorrow where you live.

I thought it was reasonably well written response, but apparently it caused some confusion (statistics and probability theory tends to have that effect on people) as someone claimed that it would NOT be raining where they were tomorrow.

I tried to set him straight and cope with my failure as a teacher and communicator.

It wasn’t until the next day that all was set right with the world.

Yesterday I recieved this IM from [name redacted to protect the innocent]: “time for the dreaded commute. 50% prob I make it home. I do or I don’t ”

It’s moments like these that make teaching so rewarding. There are few feelings in this world more rewarding that seeing a student fully and completely grasp the material that you are imparting.

So, I have decided to introduce another concept from basic stats and probability.

Probability lesson part 2: Conditional Probability

Now there are certain situation where you will encounter outcomes that are dependent on SOMETHING else happening first.

For example: what are the odds of you getting hit by lightening today?

In order to successfully calculate if you are going to get hit by lightening today, you first must break it down the components of the calculation.

If you are going to get hit by lightening, we know that it must be raining. We also know from our previous example that the odds of it raining today is 50%.

Now we need to calculate the probability of getting hit by lightening given that it’s raining. We can use a similar analysis as we did yesterday. We know that if it’s raining then either we are going to get hit by lightening or we are not. So, given that it’s raining, we can show that there is a 50% chance of getting hit by lightening.

So now that we have our two probabilities, we can multiply them together to determine our chance of getting hit by lightening today. (probability of it raining) x (probability of getting hit by lightening given that it’s raining) = .5 x.5 = .25

So there is a 25% chance of getting hit by lightening today.

For homework, everyone calculate the probability of that you could developing superpowers from getting hit by lightening today.

My friend on FB followed up with a good question about there being more “radioactive super power spiders skulking in the corners of [City redacted to protect the innocent] homes than poisonous ones. Doesn’t that drastically effect our odds?”

Now as we all know we need to break this down into it’s components in order to accurately calculate the probability of getting super powers.

So here’s your homework:

Assuming that there’s a spider in your bathtub, that you’ve washed down the drain and it’s crawled out from that little overflow hole at the top of the tub, what are the odds that you’ll get super powers?

Please show your work for full credit.