A drawer contains 6 red socks, 4 white socks, and 8 black socks. What is the probability you grab a black sock, do not return it, and then grab a red sock?
8/18 * 6/17 = ?
To calculate the probability of grabbing a black sock and then grabbing a red sock without replacement, we need to consider the total number of socks and the number of black and red socks.
Total number of socks = 6 red + 4 white + 8 black = 18 socks
Probability of grabbing a black sock on the first draw = 8 black / 18 total socks = 4/9
After removing one black sock, there are now 17 socks left in the drawer.
Probability of grabbing a red sock on the second draw = 6 red / 17 remaining socks ~= 0.353
The probability of grabbing a black sock and then a red sock without replacement is approximately (4/9) * 0.353 = 0.157 or 15.7%.
To find the probability of grabbing a black sock and then a red sock without replacement, we'll need to calculate the probabilities of each event separately and then multiply them together.
First, let's calculate the probability of grabbing a black sock on the first draw. There are a total of 6 + 4 + 8 = 18 socks in the drawer, and 8 of them are black. So the probability of picking a black sock initially is 8/18.
After picking a black sock, there are now 17 socks left in the drawer, with 6 of them being red. The probability of picking a red sock on the second draw is therefore 6/17.
To find the total probability, we multiply the probabilities of each event:
P(grabbing black sock, then red sock) = P(black sock) * P(red sock | black sock)
= (8/18) * (6/17)
≈ 0.1412
Therefore, the probability of grabbing a black sock, not returning it, and then grabbing a red sock is approximately 0.1412, or 14.12%.