SOLUTION: Harry Hose keeps all of his socks in the top drawer of his bureau. In the drawer there are four blue socks, six black socks, seven brown socks (he lost one in the laundry), and fou

Question 128019This question is from textbook Fundamentals of Mathematics
: Harry Hose keeps all of his socks in the top drawer of his bureau. In the drawer there are four blue socks, six black socks, seven brown socks (he lost one in the laundry), and four red socks. Harry reaches in a pulls a sock out at random. Find the probability that the sock chosen is
a. brown
b. blue
c. red
d. black
e. not brown
f. neither brown nor blue This question is from textbook Fundamentals of Mathematics

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
There are a total of 4 + 6 + 7 + 4 = 21 socks in the drawer.

Probability single draw is brown, 7 brown out of 21 total:

Probability blue, red, or black. Do it the same way, just change the numerator appropriately.

Probability not brown. Two ways to do this. If you draw one sock, it is either brown or not brown, so the probability that it is brown plus the probability that it is not brown is 1, or certainty. But we know the probability that it will be brown is from part a of the problem, so the probability of not brown is .

The other way is to say that there are 21 total socks, 7 of which are brown. Therefore there must be 21 - 7 = 14 socks that are not brown.

Neither brown nor blue. There are 7 brown socks and 4 blue socks for a total of 11. That means there are 21 - 11 = 10 socks that are neither brown nor blue.

Extra credit. Harry has already drawn one brown sock out of the drawer. Now, keeping that sock in his hand, he reaches in and draws out a second sock. What is the probability that he now has a matched pair?

Super-Double-Plus Extra Credit: Harry draws two socks. What is the probability that they match?
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