SOLUTION: Urn A contains 4 red and 3 black marbles. Urn B contains 5 red and 7 black marbles. From Urn A, one marble is chosen at random and placed into Urn B. Now from Urn B ( with the ext

Algebra ->  Probability-and-statistics -> SOLUTION: Urn A contains 4 red and 3 black marbles. Urn B contains 5 red and 7 black marbles. From Urn A, one marble is chosen at random and placed into Urn B. Now from Urn B ( with the ext      Log On


   

Question 1120572: Urn A contains 4 red and 3 black marbles. Urn B contains 5 red and 7 black marbles. From Urn A, one marble is chosen at random and placed into Urn B.
Now from Urn B ( with the extra marble included), two marbles are drawn at random in succession without replacement. Find the probability that they are not the same colour.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


There are two cases to consider. We have to draw one red and one black from urn B; we can draw either a red or a black from urn A.

(1) The probability of drawing a red from urn A is 4/7. Then there will be 6 red and 7 black in urn B. We need to draw 1 of the 6 red and 1 of the 7 black from urn B; the probability of that is

%28C%286%2C1%29%2AC%287%2C1%29%29%2FC%2813%2C2%29+=+%286%2A7%29%2F78+=+42%2F78+=+7%2F13

Then the probability of drawing 1 red and 1 black from urn B if a red was drawn from urn A is

%284%2F7%29%287%2F13%29+=+28%2F91

(2) The probability of drawing a red from urn A is 3/7. Then there will be 5 red and 8 black in urn B. We need to draw 1 of the 5 red and 1 of the 8 black from urn B; the probability of that is

%28C%285%2C1%29%2AC%288%2C1%29%29%2FC%2813%2C2%29+=+%285%2A8%29%2F78+=+40%2F78+=+20%2F39

Then the probability of drawing 1 red and 1 black from urn B if a red was drawn from urn A is

%283%2F7%29%2820%2F39%29+=+20%2F91

So the overall probability of drawing 1 of each color from urn B is

28%2F91%2B20%2F91+=+48%2F91

You can get some additional practice in calculating these kinds of probabilities by finding the probabilities that the two balls drawn from urn B are both red, or both black. If you find that the sum of the probabilities for all cases is 1, then you can have some confidence that your methods and calculations are good.