Question 1157932: A drawer contains 12 red socks and 8 black socks. Suppose that you choose 2 socks at random in the dark. What is the probability that you get a pair of red socks?
A drawer contains 12 red socks and 8 black socks. Suppose that you choose 2 socks at random in the dark. What is the probability that you get a pair of black socks?
A drawer contains 12 red socks and 8 black socks. Suppose that you choose 2 socks at random in the dark. What is the probability that you do not get a pair of socks?
i missed this lesson on my google meet, hoping i can get some help, thanks
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
I don't know what method(s) might have been taught at the meet you missed....
One way to work relatively simple problems like this is to use the probabilities that each sock drawn one at a time will give the desired outcome.
For getting a pair of red socks, the probability that the first is red is 12/20 and the probability the second is also red is 11/19. The probability of a pair of red socks is then (12/20)(11/19) = 132/380. Simplify the fraction, or express as a decimal, if necessary.
Use the same method to find the probability of getting a pair of black socks.
For getting two socks that don't match, you need to consider two possibilities: black then red, and red then black.
P(black, red = (8/20)(12/19) = 96/380
P(red, black) = (12/20)(8/19) = 96/380
So P(unmatched pair) = 192/380
Note that the three cases -- a pair of red, a pair of black, and an unmatched pair -- are all the possibilities, so the sum of the probabilities for the three cases should be 1.
As problems like this get more complicated, that method quickly becomes very awkward; a more sophisticated method is much easier.
Instead of calculating probabilities for each draw, we use the basic definition of probability for the whole desired outcome.
For example, for drawing a pair of red socks, the probability is
number of ways of drawing 2 of the 12 red socks (and 0 of the 8 black)
------------------------------------------------------------------------
total number of ways of drawing 2 of the 20 socks
The numerator is "12 choose 2"; the denominator is "20 choose 2":
And for getting an unmatched pair, the numerator is "12 choose 1 AND 8 choose 1":
You can use this method for calculating the probability of getting a pair of red socks.
Of course for each of the three outcomes, your answers should be the same by both methods.
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
You may look into the lesson
- A drawer contains a mixture of socks
in this site.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Solved problems on Probability".
There is a huge amount of lessons and solved problems there.
The best place to quickly observe their contents from the "bird flight height" is the lesson
- OVERVIEW of lessons on Probability
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.
Consider these lessons as your textbook, handbook, a Solutions Manual, tutorials and (free of charge) home teacher.
Happy learning (!)
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