Question

A man has four socks. Each sock is either black or white. The chances of him selecting a pair at random and that he has a white pair is 0.5. What are his chances of the pair being black?

Answer 1

Uhh 1/2 right?...

Answer 2

if the dud has 4socks, 2 black and 2 white he has a 1/2 chance of pulling to blacks

Answer 3

it dosn't say two are white two are black... 0.5 is way to easy

Answer 4

cuz if he has a 1/2 chance of pulling white than the other 1/2 goes to the black

Answer 5

this seems too easy... is this a trick question, made to confuse yourself when trying to work on it?! lol

Answer 6

i dont know its for my engineering class thats why i know it can't be 0.5

Answer 7

Well.... He has only 4 socks... and the chances of him pulling a pair (2 socks) of only white is .5 and .5 of 4 is 2..sooo the other 2 must be black..right?... im confusing myself

Answer 8

He has 2 black socks, B1 and B2, and 2 white socks, W1 and W2, listed below,
B1
B2
W1
W2

He can pull out these pairs:
B1B2
B1W1
B1W2
B2B1
B2W1
B2W2
W1B1
W1B2
W1W2
W2B1
W2B2
W2W1
There are 12 different pairs, but only 2 pairs are pairs of white socks.
The probability of taking at random a pair of white socks is 2/12 = 1/6

To have a probability of 0.5 of taking a pair of white socks, he needs to have more than 2 white socks. If he had all white socks, he'd have a 100% chance of taking a white pair, so he must have 1 black sock and 3 white socks.

Answer 9

@IsisnMozzie
The probability of taking a white pair is 0.5
What is left, 0.5, is the probability of taking a black pair or a mixed pair.

Answer 10

Ohhh... Ok. Thanks. That makes sense. I'm not confused anymore! And I bet that helped JimSacc too!

Answer 11

yeah that helped i wanna see what mathstudent is typing now

Answer 12

Now look at 3 white socks and 1 black socks:
W1
W2
W3
B1

Here are the possible outcomes:
W1W2
W1W3
W1B1
W2W1
W2W3
W2B1
W3W1
W3W2
W3B1
B1W1
B1W2
B1W3
Out of 12 possible outcomes, there are 6 pairs of white socks. We have 0.5 chance of a white pair as the problem states.
How many outcomes are black pairs?
None, since there is only one black sock.

Answer 13

awesome you are the best