The boys’ left hands: 16, 9, and almost 5 years of age. Aren’t they beautiful?

The kids didn’t even grumble too much at this photo shoot, just rolled their eyes at Mom and posed.

Do any of the readers remember Probably Handy Fun? Well, it turns out that Smurf is left-handed, like Eldest, which makes the right-handed Middle Boy unique among the brood! Unlike Eldest, who’s strongly left-handed, Smurf is more of an ambidextrous-leaning leftie: he starts to write or color with his left hand, but when he gets tired, he just switches to the right hand and keeps going! It’s pretty amazing.

Eldest is doing some elementary probability at school, so I just gave him the problems from Probably Handy Fun to solve. They are repeated here if you want to play. (Don’t peek at the solutions!)

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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 reading somewhere that it’s 1/8=12.5%,  so let’s stick with that; I know, handedness is not a completely random trait, but here 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.)

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) 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!