Question 847460: A drawer contains 2 red socks, 4 white socks, and 10 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 white and the second sock is blue?
Answer by swincher4391(1107)   (Show Source):
You can put this solution on YOUR website! The important thing is to recognize this is a "with replacement" question.
Let's figure out the entire sample size. In total there is 2+4+10 socks = 16 socks.
Next determine the probability of drawing out a white sock and drawing a blue sock.
P[white] = 4/16
Notice that after this draw, we return the sock so that we still have 16 socks. So drawing white had no effect on drawing blue next.
P[blue] = 10/16
So P[white, then blue] = P[white] * P[blue|white] = P[white] * P[blue] (because white had no effect on our chances of blue)
Then we can simply say the resulting probability is (4/16) * (10/16) = 5/32 <-- ANSWER
You do not have to keep reading but I thought I'd tweak this problem to help you understand the difference. Let's say that the problem said "you do not return it". Then we'd know this is a "without replacement" problem.
So P[white, then blue] = P[white] * P[blue|white]
We'd still find P[white] = 4/16, but notice that if we do not replace, now we have only 15 socks and 3 of them are white. This is crucial to understand.
Now P[blue|white] = 10/15 (instead of 10/16 we found earlier)
And so we'd get (4/16) * (10/15) = 1/6. We actually improved our odds since getting rid of the white on the first draw lowered the number of "bad" socks to draw on the second draw.
Hope this all makes sense!
Devin
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