Statistics introduction. I think the answer is 1/3.

Question

Once again, the electricity in my house went out as I was pulling the socks out of the dryer. I had only six single socks in there, a mix of red and blue. If I only pull out two socks the chances I pull out a red pair is 2/3. What are the chances I pull out a blue pair?

Answer 1

Write x as the number of red socks.

Write 6 − x as the number of blue socks.

Establish the probability of pulling 2 red

socks in 2 blind draws as x/6 times

(x − 1)/5 or (x² − x)/30 equal to 2/3.

Then 3(x² − x) = 60 or x² − x = 20.

Now x² − x − 20 = 0 or (x − 5) × (x + 4) = 0.

Discard x = -4 as a solution and take the

number of red socks as x = 5.

This would force the number of blue socks

to 1, giving the probability of extracting a

blue pair in only 2 blind draws as zero.