Day: November 13, 2021

From the Academic Jungle Archives: Probably Handy Fun

So I dug through my old posts over at the defunct Academic Jungle (*cough-cough* that electronic dust is killing my sinuses). 
This one from 2012 (!) makes for some fun Saturday content. Btw, Smurf is now 10 and is left-handed, like his oldest bro. 

Having kids, especially little ones, is a source of enormous joy and tremendous exhaustion. There are many activities that are not particularly fun for anyone involved (e.g. projectile vomiting and associated cleanup) or are fun for the kids, but not so much for the parent (e.g. watching Teletubbies yet again with the 3rd kid, making it roughly my 11,678th viewing. I hate Tinky Winky and Dipsy with the burning passion of a thousand suns. Lala is still cool, though.)

Surfing the web on my phone or simply thinking about work are my favorite passtimes during protracted mind-numbing activities. This morning, while I was nursing Baby Smurf but — alas! — did not have my phone handy, I started thinking about the fact that Baby Smurf seems like he might be left-handed, although it may be too soon to say with certainty. He usually likes to hold two things at the same time, one in each hand, but he is much more likely to drop an old object and pick up a new, more interesting one with his left hand. Our eldest son is a left-handed, our middle one right-handed. Of course, all this leads to some cute probability questions. [1]

Here is what we know: let’s say that 1 in 8 people are left-handed (quick googling puts the percentage between 8 and 15%, and I remember a few years ago and reading somewhere that it’s 1/8=12.5% , so let’s stick with that). [2]

1) What is the probability that a family with three children will have a left-handed child? (meaning at least one)

2) What is the probability that a family with three children will have exactly two left-handed children?

3) What is the probability that a family with three children will have (at least) two left-handed children?

4) What is the probability that someone’s first and third child will be left-handed? (The only assumption is that the person will in fact have at least 3 kids.)

5) If my first child is left-handed and my second child is right-handed, what is the probability that my third child will be left-handed?

6) (added this one a bit later) If my first child is left-handed, what is the probability that I will have (at least) another left-handed child out of three total?

Have fun!

(I will post the solution in a day or so, although I am sure we’ll have the correct answers before that.)

[1] I admit this post was inspired by this one at Bad Mom, Good Mom, found through a link at Cloud’s.
[2] As badmomgoodmom says in the comments to the original post, handedness is not a completely random trait. Here, however, I just wanted us to have some fun with probabilities, so let’s assume handedness is a discrete random variable, with values L and R having the probabilities of 1/8 and 7/8, respectively.