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?
To find the probability of selecting a red marble, replacing it, and then selecting a blue marble, we need to know the total number of marbles and the number of red and blue marbles. Let's assume there are 10 marbles in total, with 4 red marbles and 6 blue marbles.
(a) Probability of selecting a red marble, replacing it, and then selecting a blue marble:
The probability of selecting a red marble on the first draw is 4/10.
Since we replace the marble after the first draw, the probability of selecting a red marble again on the second draw is also 4/10.
The probability of selecting a blue marble on the second draw is 6/10.
To find the total probability, we multiply the individual probabilities:
(4/10) * (4/10) * (6/10) = 96/1000 = 0.096
Therefore, the probability of selecting a red marble, replacing it, and then selecting a blue marble is 0.096.
(b) Probability of selecting a red marble, setting it aside, and then selecting a blue marble:
The probability of selecting a red marble on the first draw is 4/10.
Since we set it aside and don't replace it, there are now 9 marbles left, with 3 red and 6 blue.
The probability of selecting a blue marble on the second draw is 6/9.
To find the total probability, we multiply the individual probabilities:
(4/10) * (6/9) = 24/90 = 4/15 = 0.267
Therefore, the probability of selecting a red marble, setting it aside, and then selecting a blue marble is 0.267.
The answers to parts (a) and (b) are different. This is because in part (a), we replace the marble after each draw, which means the pool of marbles remains the same for each draw. In part (b), we set aside the red marble, reducing the total number of marbles for the second draw, which changes the probability distribution.
To find the probability of selecting a red marble, replacing it, and then selecting a blue marble, we need to know the number of red marbles and blue marbles in the bag.
Let's say there are 5 red marbles and 10 blue marbles in the bag. The probability of selecting a red marble would be 5/15 (since there are 5 red marbles out of a total of 15 marbles). After replacing the red marble, the probability of selecting a blue marble would still be 10/15 (since there are still 10 blue marbles out of a total of 15 marbles after replacing the red marble).
To find the overall probability, we multiply the individual probabilities together. So the probability of selecting a red marble, replacing it, and then selecting a blue marble would be (5/15) * (10/15) = 1/3.
To find the probability of selecting a red marble, setting it aside, and then selecting a blue marble, we need to know the same information about the number of red and blue marbles in the bag.
Using the same example, the probability of selecting a red marble would be 5/15 (since there are 5 red marbles out of a total of 15 marbles). After setting the red marble aside, we are left with 14 marbles in the bag, of which 10 are blue. So the probability of selecting a blue marble would be 10/14.
Again, to find the overall probability, we multiply the individual probabilities together. So the probability of selecting a red marble, setting it aside, and then selecting a blue marble would be (5/15) * (10/14) ≈ 0.2381.
The answers to parts (a) and (b) are not the same. In part (a), when the red marble is replaced, the number of red and blue marbles remain the same for the second selection. However, in part (b), when the red marble is set aside, the number of marbles changes for the second selection. This leads to different probabilities for selecting a blue marble in each case, resulting in different overall probabilities.