David has two boxes containing shapes.
In box A there are 4 stars and 2 hearts.
In box B there are 2 stars and 1 heart.
David takes, at random, a shape from box A and puts it into box B.He then takes a shape from box B.
What is your question?
To determine the probability of selecting a particular shape after David's actions, we need to calculate the probability of each shape being chosen from each box and then combine those probabilities.
Let's start with the initial setup:
In box A, there are 4 stars and 2 hearts, making a total of 6 shapes.
The probability of selecting a star from box A is 4/6 since there are 4 stars out of 6 total shapes.
Similarly, the probability of selecting a heart from box A is 2/6.
Moving on to box B after David transfers a shape from box A:
Now, box B contains the transferred shape along with its original 2 stars and 1 heart (which were in box B initially).
So, in box B, there are now 3 stars and 2 hearts, making a total of 5 shapes.
The probability of selecting a star from box B depends on which shape was transferred from box A. If a star was transferred, box B would have 4 stars out of 5 shapes, giving a probability of 4/5.
However, if a heart was transferred, box B would have 3 stars out of 5 shapes, resulting in a probability of 3/5.
Therefore, to calculate the overall probability of selecting a particular shape after David's actions:
The probability of selecting a shape from box A is multiplied by the probability of transferring that shape to box B.
Then, the probability of selecting a shape from box B, after the transfer, is multiplied by the result from the previous step.
Let's illustrate this with an example:
Suppose we want to find the probability of selecting a star from box B.
First, we calculate the probability of transferring a star from box A to box B, which is 4/6 (the probability of selecting a star from box A since all stars remain in box A).
Second, we calculate the probability of selecting a star from box B after the transfer. Given that a star was transferred, we have 4 stars out of 5 shapes in box B. Therefore, the probability is 4/5.
Finally, we multiply the two probabilities together:
(4/6) * (4/5) = 16/30 = 8/15.
Thus, the probability of selecting a star from box B after David's actions is 8/15.