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May 2nd, 2015, 03:27 AM   #1
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Question Moving balls between bags - stumped!

Bag A contains 3 red balls and 7 green balls. Bag B contains 7 red and 8 green balls.
A ball is taken out of bag A and placed in bag B. Then a ball is taken out of B.

a) Calculate that both the balls are red.
P(A is red) = 3/10 then, since A has to come out we add the
red to bag B and it has 8 red and 8 green so the probability
of the second even is P(B is red) = 8/16.
So P = (3/10).(8/16) = (3/10).(1/2) = 3/20


b) Both balls are green
Same sort of reasoning gives (7/10).(9/16) = 63/160

c) At least one ball is green
Here I'm flummoxed. I'm missing some reasoning.

d) At least one is not green.
Here I'm flummoxed. I'm missing some reasoning.
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May 2nd, 2015, 07:11 AM   #2
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(a) and (b) are correct. Very good!

In general, if "X", "Y", "Z" are mutually exclusive events then P(X or Y or Z)= P(x)+ P(y)+ P(Z).
Here we can take X to be "the first ball is red and the second is green" There are initially 3 red balls out of 10 so the probability the first ball is red is 3/10. Now there are 9 balls, 7 of which are green. The probability the second ball is green is 7/9. P(X)= (3/10)(7/9)= 7/30.

Take Y to be "the first ball is green and the second is red". There are 7 green balls out of 10 so the probability the first ball is green is 7/10. Now there are 9 balls, 3 of which are red. The probability the second ball is red is 3/9. P(Y)= (7/10)(3/9)= 7/30.

Take Z to be "both balls are red" As you calculated before, P(Z)= 3/20.

The probability "at least one ball is not green" is 7/30+ 7/30+ 3/20= 14/60+ 14/60+ 9/20= 37/60.
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May 2nd, 2015, 08:08 AM   #3
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Hello, ofransen!

Quote:
Bag A contains 3 red balls and 7 green balls.
Bag B contains 7 red and 8 green balls.
A ball is taken out of bag A and placed in bag B.
Then a ball is taken out of B.
Calculate the probability that:

a) Both balls are red.



b) Both balls are green.

Quote:
c) At least one ball is green.

The opposite of "at least one green" is "no green" or "both red".




Quote:
d) At least one is not green.

The opposite of "At least one not green" = "Both green"



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May 3rd, 2015, 12:48 AM   #4
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Oh it's so easy when explained! I knew I was missing something...
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