Question 1038736: Given 2 bags A and B. suppose A contains 3 white balls and 5 blue balls and B contains 4 white balls and 3 blue balls, if a ball is drawn from A and is placed unnoticed in B. determine the probability that a ball drawn from B is blue.
Found 2 solutions by Boreal, Theo:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! probability of blue ball from A drawn is (5/8). If put into B, the probability of a blue ball from B is now 1/2.
probability of white ball from A is (3/8). If put into B, the probability of a blue ball from B is 3/8.
With a tree diagram
W 3/8-------------------B 5/8
B 3/8 W 5/8-------------B1/2--W1/2
Their product
9/64,15/64------------20/64---20/64=1 that needs to check.
The probability of blue being drawn from B is 29/64
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! A contains 3 white and 5 blue.
B contains 4 white and 3 blue
a ball is drawn randomly from A and placed into B.
what is the probability that a ball subsequently drawn from B is blue.
the probability that the ball drawn from A is blue is 5/8.
therefore there is a 5/8 probability that the ball placed into B is blue, and there is a 3/8 probability that the ball placed into B is white.
what this says is that, if you could do this an infinite number of time, then 5/8 of the time the ball will be blue and 3/8 of the time the ball will be white.
5/8 of the time, the probability of getting a blue ball out of B will be 4/8.
3/8 of the time, the probability of getting a blue ball out of B will be 3/8.
the probability of getting a blue ball out of B should be 5/8 * 4/8 + 3/8 * 3/8.
this would be equal to 29/64.
make the probability simpler and it will be easier to see how it works.
assume 2 white balls and 1 black ball in A.
assume 1 white ball and 1 black ball in B.
if the formula works, then 2/3 of the time you will have 2 white balls and 1 black ball in B which give you the probability that you get a black ball out of B 1/3, and .....
1/3 of the time you will have 1 white ball and 2 black balls in B which give you the probability that you get a black ball out of B 2/3.
the total probability should therefore be 2/3 * 1/3 + 1/3 * 2/3 = 4/9.
the following tree diagram shows you that this is correct.
it is sometimes useful to look at these problems as percent problems rather than probability problems.
percents and probabilities are very closely related.
if something happens 90% of the time, then the probability it will happen again is 90%.
in this particular case, 5/8 of the time, the ball placed in bag B will be blue and 3/8 of the time the ball placed in bag B will be white.
therefore 5/8 of the time the probability of drawing a blue ball out of bag B will be 4/8, and 3/8 of the time the probability of drawing a blue ball out of bag B will be 3/8.
this means that 5/8 * 4/8 = 20/64 of the time you will draw a blue ball out of bag B and 3/8 * 3/8 = 9/64 of the time you will draw a blue ball out of bag B which makes the total time you will draw a blue ball out of bag B equal to 29/64.
that means the probability of drawing a blue ball out of B after taking a ball out of bag A at random equal to 29/64.
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