In a jar there are 4 red marbles 5 green marbles and 7 blue marbles.
1 what us the probability of selecting a red marble replacing it and then selecting a blue marble
2 What is the probability of selecting a red marble setting it aside and then selecting a blue marble
3 are the answers to part 1 and 2 the same why or why not
This is the only question i have on my school work if any one can plz help me that would be awesome
Ok so
There are 4 red marbles.
There are 7 blue marbles.
There are 5 green marbles.
There are 16 marbles in total.
a.
Answer = (probability of selecting a red marble)(probability of selecting a blue marble)
First, the probability of selecting a red marble.
Next, the probability of selecting a blue marble.
Multiply the probabilities together.
That is the probability for event a.
b.
Answer = (probability of selecting a red marble)(probability of selecting a blue marble)
First, the probability of selecting a red marble.
Next, the probability of selecting a blue marble WITH A RED MARBLE REMOVED.
Multiply the probabilities together.
That is the probability for event b.
c.
Obviously:
So the answer is no.
16 marbles
1. independent red * blue = 4/16 * 7/16
2. dependent red then blue = 4/16 * 7/15
3.in number two the probability of blue is impacted by the fact that you have taken a marble out. The two draws are not independent on problem 2
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1. To find the probability of selecting a red marble, replacing it, and then selecting a blue marble, you need to consider the total number of marbles and the number of red and blue marbles in the jar.
First, we add up the total number of marbles: 4 red + 5 green + 7 blue = 16 marbles.
The probability of selecting a red marble is 4/16 since there are 4 red marbles out of 16 total marbles.
Since we are replacing the red marble back into the jar, the number of red marbles doesn't change for the second draw. Hence, we still have 4/16 probability of selecting a red marble for the second draw.
Similarly, the probability of selecting a blue marble is 7/16 since there are 7 blue marbles out of 16 total marbles.
Now, to find the probability of both events happening, we multiply the probabilities together: (4/16) * (7/16) = 28/256.
Therefore, the probability of selecting a red marble, replacing it, and then selecting a blue marble is 28/256.
2. To find the probability of selecting a red marble, setting it aside, and then selecting a blue marble, we follow a similar approach as above.
The probability of selecting a red marble is still 4/16 since there are 4 red marbles out of 16 total marbles.
However, after selecting and setting aside the red marble, we now have one less marble in the jar. So, the total number of marbles for the second draw is 16 - 1 = 15.
The probability of selecting a blue marble is now 7/15 since there are 7 blue marbles out of 15 remaining marbles.
To find the probability of both events happening, we multiply the probabilities together: (4/16) * (7/15) = 28/240.
Therefore, the probability of selecting a red marble, setting it aside, and then selecting a blue marble is 28/240.
3. The answers to part 1 and part 2 are not the same. In part 1, we replaced the red marble after the first draw, which means the total number of marbles in the jar remains the same (16). In part 2, we set aside the red marble, so the total number of marbles for the second draw decreases to 15. This difference in the total number of marbles affects the probability of selecting a blue marble in the second draw. Hence, the probabilities and the final answers for part 1 and part 2 are different.