Question 1039124: A CONTAINER IS FILLED WITH 5 BOTTLES OF WHITE WINE, 3 BOTTLES OF RED WINE AND 1 BOTTLE OF GRAPE JUICE. IF TWO BOTTLES ARE WITHDRAWN WITH REPLACEMENT ,WHAT IS THE PRABABILITY THAT ONE OF THE BOTTLES CONTAIN A GRAPE JUICE
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! my previous answer was in error because it assumed no replacement.
with replacement, the answer is as follows:
the probability of getting a grape bottle on any draw is 1/9.
this is because there are 9 bottles total, only 1 of which is a grape bottle.
the probability of getting a grape bottle on the first draw only is therefore 1/9 * 8/9. = 8/81.
the probability of getting a grape bottle on the second draw only is therefore 8/9 * 1/9 = 8/81.
the probability of getting a grape bottle on the first draw and a grape bottle on the second draw is equal to 1/9 * 1/9 = 1/81.
the probability of not getting a grape bottle on the first draw and not getting a grape bottle on the second draw is 8/9 * 8/9 = 64/81.
the total of all probabilities should be equal to 1.
you get 8/81 + 8/81 + 1/81 + 64/81 = 81/81 = 1, as it should be.
you were asked for the probability that only one of the bottles contains grape.
that would be 8/81 + 8/81 = 16/81.
you do not include the probability of getting 2, because then you would have been asked for the probability of at least one of the bottles containing grape.
that's not what was asked.
the assumption is that you were asked for the probability of getting one and only one out of the 2 draws.
that's my interpretation.
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