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May 19th, 2017, 12:38 AM   #1
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Bags problem

You have 2 bags, A and B
In bag A there's 3 white balls and 2 black balls
In bag B there's 1 white balls and 3 black balls

If you take only one ball from each bag, what is the probability that you will get one white ball and one black ball?

Remember that there are two different combinations:
A:3/5 and 3/4 = 45%
B:1/4 and 2/5 = 10%

Is the answer the average of 45 and 10 or are you supposed to just add them up?
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May 19th, 2017, 04:06 AM   #2
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b,w : 2/5 * 1/4 = 2/20
w,b : 3/5 * 3/4 = 9/20

add 'em: 11/20
multiply 'em: 18/400 = 9/200

SO?
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May 19th, 2017, 04:03 PM   #3
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to be formal it's

$p = \dfrac{\dbinom{3}{1}}{\dbinom{5}{1}} \dfrac{\dbinom{3}{1}}{\dbinom{4}{1}}+\dfrac{ \dbinom{1}{1}}{\dbinom{4}{1}} \dfrac{\dbinom{2}{1}}{\dbinom{5}{1}}=\dfrac{11}{20 }$
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May 19th, 2017, 05:13 PM   #4
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Math Focus: Yet to find out.
Bags bags bags.. they're very useful things..
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