SOLUTION: A drawer contains 4 red socks, 6 white socks, and 8 blue socks. Without looking, you draw out a sock, return it, and draw out a second sock. What is the probability that the first

Algebra ->  Probability-and-statistics -> SOLUTION: A drawer contains 4 red socks, 6 white socks, and 8 blue socks. Without looking, you draw out a sock, return it, and draw out a second sock. What is the probability that the first       Log On


   

Question 974002: A drawer contains 4 red socks, 6 white socks, and 8 blue socks. Without looking, you draw out a sock, return it, and draw out a second sock. What is the probability that the first sock is red and the second sock is blue
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
4%2B6%2B8=18 , so there are 18 socks in the drawer.
Since 4%2F18=2%2F9 of them are red,
and any sock is as likely to be picked as any other,
the probability that the first sock picked is red is 2%2F9 .
Before the second pick, there are 18 socks in the drawer.
Since 8%2F18=4%2F9 of them are blue,
and any sock is as likely to be picked as any other,
the probability that the second sock picked is blue is 4%2F9 .
Whatever happened during the fist pick does not matter .
The two events are independent (and your teacher says to multiply the two probabilities when events are independent).
There is a good logical reason for multiplying:
For a first pick, 2%2F9 of the times you would get a red sock,
and 4%2F9 of those times, your second pick would be blue.
So 4%2F9 of 2%2F9 = %284%2F9%29%282%2F9%29=8%2F81 of the times
you would pick a red sock on your first try and a blue sock on your second pick.
The probability of that chain of events is highlight%288%2F81%29 .