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?
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!
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.
+758 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.
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,
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.
