# Math Dad vs Science Mom 36: Black Socks

I’m Science Mom. This is Math Dad, and
we’re back for another challenge problem this was number… 36? 36 right and you can
join us in the description of the video there’s a little link to desmos and
you can log right in it’s free and you can try it with me. Be sure to pause the
video so you have a chance to work on it before you see me solve it. Alright let’s
look at the problem. It’s called black socks. It’s a fairly simple problem there
are three drawers in this dresser. one drawer contains two white socks, one
drawer contains two black socks, and the final drawer contains one black sock and one white sock. Okay. So turn off the lights and you randomly select a drawer and then without looking you reach in and you grab a sock and you see that
it’s a black sock so the question is what is the probability that the other
sock in that drawer is black? Oh boy. You understand the question? I do it’s been a
while since I’ve done probability Alright, because I’m only giving you two minutes. Okay. For those of you watching now would be a great time to pause the video
science mom’s time begins Now. All right. So I don’t know which drawer has been
opened. It could be it could be this one or this one.
It can’t be that one because I only would have drawn out a white sock, so one
of those got opened and a black sock was pulled I’m just gonna start off with
saying so here’s option number one assume I
opened this door and got rid of that black sock um… and… uhhhhhh what’s the probability
that the other sock in that drawer is black. So probability for choice orange
would be zero there’s no-i-cuz it’s gonna be white. All right choice purple is I
opened up this drawer right here and took out a black sock and there’s a if
that was the case then 100% chance the the other sock would be black but I
don’t know which drawer I opened and it would seem sort of reasonable
split zero and a hundred percent and say fifty.
No, but there’s a third drawer but can I just I think I could just like totally
discount that drawer because I pulled out a black sock. So that I’m gonna say
that the way the answer supposed to be one half. No, try again. Nuts! Alright. ummmmmmm. I’m gonna delete that because that no try again is discouraging. Yeah you fell for the trap. I fell for the trap so does that mean I
can’t ignore the third drawer? No no you can eliminate the third drawer that’s
fine you actually should eliminate the third drawer. you know you did not pull from the-aw man, time’s up I’m not done with the problem though don’t tell me so I pulled out a
black sock so I know it had to be one of these two drawers that I pulled a sock
from and if it was this drawer then I will pull out a white sock and a sister
I will put a black sock what’s the chance that it’s this drawer that’s
really what I’m asking what’s being asked. Told you in a while since I’ve
done probabilities but it just yeah so that’s a good trip
cuz it seems like it should be one half to me. Yeah, this is a conditional
probability question. Let me ask you this: are the three black socks equally likely
to have been the sock you chose no this one it’s more like this one because each
of the three black socks is equally likely to have been chosen right yes
okay so out of those three two of them are in a drawer with a second black sock
therefore the probability of a black sock paper is 2/3 yeah two out of three
times you’re going to end up with a black sock as the other sock in
the drawer Bertrand’s box paradox yep famous enough paradox that it has a name *Math dad wins, the score is now 19-17

## One thought on “Math Dad vs Science Mom 36: Black Socks”

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