Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
The diagram below shows the contents of a jar from which you select marbles at random.
An illustration of a jar of marbles is shown. Four of the marbles are labeled with an upper R, seven of the marbles are labeled with an upper B, and five of the marbles are labeled with an upper G. The key identifies upper R to represent red marbles, upper B to represent blue marbles, and upper G to represent green marbles.
What is the probability of selecting a red marble, replacing it, and then selecting a blue marble? Show your work.
What is the probability of selecting a red marble, setting it aside, and then selecting a blue marble? Show your work.
Are the answers to parts (a) and (b) the same? Why or why not?
i tried looking it up but nobody had answered
yes, mathhelper already gave you the answer, in your previous post.
They are not the same because you have a bigger population to choose from if you put the first one back and therefore your chance of getting what you want goes down.
To find the probability of selecting a red marble, replacing it, and then selecting a blue marble, we can use the concept of independent events. On the first draw, there are 4 red marbles out of a total of 16 marbles. Therefore, the probability of selecting a red marble on the first draw is 4/16.
Since the marble is replaced, the total number of marbles remains the same for the second draw. Now, there are 7 blue marbles out of 16 remaining marbles. Therefore, the probability of selecting a blue marble on the second draw is 7/16.
To find the overall probability of both events happening, we multiply the individual probabilities together. So, the probability of selecting a red marble, replacing it, and then selecting a blue marble is (4/16) * (7/16) = 28/256, which simplifies to 7/64.
To find the probability of selecting a red marble, setting it aside, and then selecting a blue marble, we need to consider that the marble is not replaced after the first draw. So, for the first draw, the probability of selecting a red marble is still 4/16.
However, after setting the red marble aside, the total number of marbles is reduced to 15. Out of these 15 marbles, there are still 7 blue marbles. Therefore, the probability of selecting a blue marble on the second draw, given that a red marble was set aside, is 7/15.
Again, we multiply the individual probabilities together to find the overall probability. So, the probability of selecting a red marble, setting it aside, and then selecting a blue marble is (4/16) * (7/15) = 28/240, which simplifies to 7/60.
The answers to parts (a) and (b) are different. In part (a), the marbles are replaced after each draw, whereas in part (b), the marbles are not replaced. This difference affects the denominator of the probability calculation in each step.
In part (a), the denominator remains the same for both draws (16 marbles). But in part (b), the denominator changes after the first draw, as the set-aside marble is no longer included in the available marbles for the second draw.
Therefore, the probabilities in part (a) and part (b) are different due to the change in the sample space or the set of possible outcomes for the second draw.