The contents of a jar holds 4 red marbles, 7 blue marbles, and 5 green marbles from which you select marbles at random.
What is the probability of selecting a red marble, replacing it, and then selecting a blue marble? Show your your work.
Is it 4/16 for picking red then 7/16 for picking blue?
What is the probability of selecting a red marble, setting it aside, and then selecting a blue marble? Show your work.
Is it 4/16 for red then seeing it aside and picking blue 7/15?
Are the answers to parts (a) and (b) the same? Why our why not?
I would say no because there are two different probabilities. Am I correct on all three answers, if not please help.
wow she's still waiting to this day
Still waiting.....
Let's go through each part step-by-step:
(a) Probability of selecting a red marble, replacing it, and then selecting a blue marble:
To calculate the probability, we multiply the individual probabilities together.
The probability of selecting a red marble is 4/16, as there are 4 red marbles out of a total of 16 marbles.
Since we are replacing the marble after each selection, the total number of marbles remains the same for the second selection. Therefore, the probability of selecting a blue marble is also 7/16.
So, the probability of selecting a red marble, replacing it, and then selecting a blue marble is (4/16) * (7/16) = 28/256 = 7/64.
(b) Probability of selecting a red marble, setting it aside, and then selecting a blue marble:
To calculate the probability, we need to consider the updated number of marbles after the first selection.
The probability of selecting a red marble is still 4/16, as before.
After setting aside the red marble, we are left with a total of 15 marbles for the second selection (since one marble has been removed).
The probability of selecting a blue marble from the remaining 15 marbles is 7/15.
So, the probability of selecting a red marble, setting it aside, and then selecting a blue marble is (4/16) * (7/15) = 28/240 = 7/60.
(c) Are the answers to parts (a) and (b) the same?
No, the answers to parts (a) and (b) are not the same. The key difference is that in part (a), we replaced the marble after each selection, while in part (b), we did not replace the first marble that was selected.
Replacing the marble after each selection in part (a) keeps the total number of marbles constant, resulting in the same denominator for both probabilities. But in part (b), selecting a red marble and setting it aside reduces the total number of marbles for the second selection, leading to a different probability.
So, the correct answers are 7/64 for part (a) and 7/60 for part (b).
To find the probability of two independent events happening sequentially, you multiply the probabilities of each event.
(a) For the first part, you want to find the probability of selecting a red marble, replacing it, and then selecting a blue marble.
The probability of selecting a red marble is 4 out of 16, since there are 4 red marbles out of a total of 16 marbles. When you replace the first marble, the total number of marbles remains the same.
So the probability of selecting a red marble and replacing it is 4/16.
The probability of selecting a blue marble is 7 out of 16, as there are 7 blue marbles out of the total 16 marbles.
To find the probability of both events happening, you multiply the probabilities together:
P(red and blue) = P(red) * P(blue) = (4/16) * (7/16) = 28/256 = 7/64
So the correct answer is 7/64.
(b) For the second part, you want to find the probability of selecting a red marble, setting it aside, and then selecting a blue marble.
The probability of selecting a red marble is still 4/16. However, after selecting the red marble, you set it aside, which means the total number of marbles decreases by 1.
So for the second selection, there are now only 15 marbles remaining, with 7 of them being blue.
The probability of selecting a blue marble from the remaining marbles is 7/15.
To find the overall probability of both events happening, you multiply the probabilities:
P(red and blue) = P(red) * P(blue) = (4/16) * (7/15) = 28/240 = 7/60.
So the correct answer is 7/60.
Therefore, the answers to parts (a) and (b) are different. In part (a), you replace the first marble, so the probability remains the same. In part (b), you set aside the first marble, so the probability changes for the second selection.