Brent starts with $16$ identical white socks in his sock drawer. Imagine he receives $2$ identical black socks as a gift and mixes them in with his $16$ white socks. If he draws one sock without looking to put on his left foot, then draws a second sock without looking to put on his right foot, what is the probability that he draws mismatched socks?

Guest Jul 26, 2023

#1**0 **

The probability of Brent drawing mismatched socks is the sum of the probabilities of two mutually exclusive events: drawing a white sock on the left foot and a black sock on the right foot, or drawing a black sock on the left foot and a white sock on the right foot.

The probability of drawing a white sock on the left foot is 18/20, since there are 18 total socks and 18 white socks.

The probability of drawing a black sock on the right foot is 2/18, since there are 2 black socks and 18 total socks remaining after the first sock is drawn.

Therefore, the probability of drawing a white sock on the left foot and a black sock on the right foot is 18/20*2/18=1/5.

Similarly, the probability of drawing a black sock on the left foot and a white sock on the right foot is also 1/5.

Therefore, the probability of Brent drawing mismatched socks is 1/5 + 1/5 = 2/5.

Hope this helps!

Guest Jul 26, 2023

#2**0 **

Umm.... I think that's wrong because there are WAY less black socks than white, so I think the probability should be smaller, but thanks anyway.

Guest Jul 26, 2023

edited by
Guest
Jul 26, 2023

#3**0 **

Hmmm. So, we can see that there are 16 white socks and 2 black socks. There are 18 socks in total. 16 / 18 that he draws white. Then, we multiply 16 / 18 by 2 / 17. It is 2 / 17 instead of 2 / 18 because we already taken a white sock. When we multiply them together, we get 16 / 153. Then, we do it the other way around. We have a 2 / 18 chance of getting a black sock. Then, we have a 16 / 17 chance of getting a white sock. When we multiply them together, we get 16 / 153 again. Therefore, we multiply 16 / 153 * 2, or **32 / 153**.

history Jul 26, 2023

#4**0 **

If Brent draws a white sock with his left foot, then he can draw either a white or a black sock with his right foot to have mismatched socks. Likewise, if he draws a black sock with his left foot, he can draw a white or a black sock with his right foot to have mismatched socks. So, there are 2×2=4 ways for Brent to draw mismatched socks.

The total number of possible outcomes is 18×18=324 because there are 18 socks total and 18 possibilities for each draw. So, the probability that Brent draws mismatched socks is 4/324 = 1/81,

Guest Jul 27, 2023

#6**0 **

There are 18 total socks in the drawer, and 2 of them are black. There are two ways to draw mismatched socks: he can draw a black sock on the left foot and a white sock on the right foot, or he can draw a white sock on the left foot and a black sock on the right foot.

The probability of drawing a black sock on the left foot and a white sock on the right foot is 2/18⋅16/17=8/153.

The probability of drawing a white sock on the left foot and a black sock on the right foot is also 8/153.

So, the probability of drawing mismatched socks is 8/153+8/1538=16/153.

Guest Jul 28, 2023