A pile of socks has 12 green socks, 4 blue socks, and 8 purple socks. A sock is chosen at random, not replaced, then a second sock is chosen.
Which expression can be used to determine the probability that both socks are
green?
A.12/24 * 2/24
B.12/24 *11/23
C.12/24 * 11/24
D.12/24 * 4/24
The probability of choosing one green sock from the pile of socks is 12/24, as there are 12 green socks out of a total of 24 socks.
After one green sock has been chosen and not replaced, there are 23 socks left, out of which 11 are green socks. So, the probability of choosing a second green sock is 11/23.
To find the probability of both socks being green, we multiply the probability of choosing one green sock by the probability of choosing a second green sock, given that the first sock was green.
Therefore, the expression that can be used to determine the probability that both socks are green is:
B. 12/24 * 11/23
This simplifies to:
B. 1/2 * 11/23
= 11/46
Therefore, the probability that both socks are green is 11/46.