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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?
a) Probability of selecting a red marble, replacing it, and then selecting a blue marble:
P(RB) = P(R) x P(B) = (4/16) x (7/16) = 0.1094 or 10.94%
b) Probability of selecting a red marble, setting it aside, and then selecting a blue marble:
P(RB) = P(R) x P(B|not R) = (4/16) x (7/15) = 0.0933 or 9.33%
The answers to parts (a) and (b) are not the same because in part (a) the red marble is replaced before selecting the blue marble, meaning that the probability of getting a red marble remains the same for the second draw. However, in part (b) the red marble is not replaced, so the probability of getting a blue marble changes because there is now one less marble in the jar.
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A box contains 95 pink rubber bands and 90 brown rubber bands. You select a rubber band at random from the box. Find each probability. Write the probability as a fraction in simplest form.
Find the theoretical probability of selecting a pink rubber band.
Find the theoretical probability of selecting a brown rubber band.
You repeatedly choose a rubber band from the box, record the color, and put the rubber band back in the box. The results are shown in the table below. Find the experimental probability of each color based on the table.
Outcome Occurrences
Pink 36
Brown 33
a) Theoretical probability of selecting a pink rubber band:
P(pink) = # of pink rubber bands / total # of rubber bands
P(pink) = 95 / (95 + 90)
P(pink) = 19/38
b) Theoretical probability of selecting a brown rubber band:
P(brown) = # of brown rubber bands / total # of rubber bands
P(brown) = 90 / (95 + 90)
P(brown) = 18/38
Experimental probability of selecting a pink rubber band:
P(pink) = # of occurrences of pink rubber band / total # of trials
P(pink) = 36 / (36 + 33)
P(pink) = 12/23
Experimental probability of selecting a brown rubber band:
P(brown) = # of occurrences of brown rubber band / total # of trials
P(brown) = 33 / (36 + 33)
P(brown) = 11/23
To calculate the probability of selecting a red marble, replacing it, and then selecting a blue marble, we need to find the individual probabilities and multiply them together.
Step 1: Find the probability of selecting a red marble.
The jar contains 4 red marbles out of a total of 4+7+5=16 marbles.
So, the probability of selecting a red marble is 4/16 or 1/4.
Step 2: Find the probability of selecting a blue marble.
After replacing the red marble, the total number of marbles remains the same.
The jar still contains 7 blue marbles out of a total of 16 marbles.
So, the probability of selecting a blue marble is 7/16.
Step 3: Multiply the two probabilities together.
The probability of selecting a red marble and then a blue marble is (1/4) * (7/16) = 7/64.
Now, let's calculate the probability of selecting a red marble, setting it aside, and then selecting a blue marble.
Step 1: Find the probability of selecting a red marble.
As calculated earlier, the probability of selecting a red marble is 1/4.
Step 2: Find the probability of selecting a blue marble after setting aside the red marble.
After setting aside the red marble, the total number of marbles decreases to 16-1=15.
The jar still contains 7 blue marbles out of a total of 15 marbles.
So, the probability of selecting a blue marble is 7/15.
The probability of selecting a red marble and then a blue marble (without replacement) is (1/4) * (7/15) = 7/60.
No, the answers to parts (a) and (b) are not the same. This is because when we replace the red marble before selecting the blue marble, the probability of selecting a blue marble remains the same. But when we set aside the red marble and then select a blue marble without replacement, the total number of marbles decreases, affecting the probability.