Question

Charlie has 13 socks in his drawer, 7 blue and 6 green. He selects 5 socks at random. Find the probability that he gets

d. The one sock that has a hole in it.

Answer 1

\[P(selects\ the\ 1\ with\ hole)=\frac{12C4}{13C5}\]

Answer 2

so you take one away from 13 and 5 so its going to be 12C4/13C5

Answer 3

???

Answer 4

there is only one sock with a hole in it right?

Answer 5

oh nvm sorry

Answer 6

YES THATS CORRECT THERES ONLY ONE HOLE IN THE SOCK

Answer 7

one with the hole four without @kropot72 has it

Answer 8

Only one sock out of the 13 socks has a hole. So the probability of getting the one sock with a hole in a random sample of 5 socks is the number of combinations of 12 socks taken 4 at a time divided by the number of combinations of 13 socks taken 5 at a time.

Answer 9

i misread
one way to choose the one sock with a hole, \(\binom{12}{4}\) ways to choose the other four

Answer 10

Great thanks!

Answer 11

You're welcome :)

Answer 12

This sort of problem is usually easiest to work backwards (find the probability of him not finding the one with the hole)
\[\frac{ 25 * 24 * 23 * 22 * 21 }{ 26 * 25 * 24 * 23 * 22 } \]
Then simplifying, there is a 21/26 chance that he will not grab the sock with the hole, and thus a 5/26 chance that he will grab the sock with the hole in it.