A marble is drawn from a bag containing four white, three red, and two blue marbles. Without replacing the first marble, a second marble is drawn.
a. Draw a two stage outcome tree for this experiment.
b. Turn the outcome tree into a probability tree diagram by labeling all of the branches with the appropriate probabilities.
c. Determine the probability of each outcome by using the multiplicative property of probability.
d. Find the probability of getting a red and a white marble by using the additive property of probability.
Thanks so much! I am very confused on the difference in the trees and branches?
https://www.google.com/search?client=safari&rls=en&q=Statistical+trees+branches&ie=UTF-8&oe=UTF-8
No problem! I'll break it down for you step by step.
a. To create a two-stage outcome tree for this experiment, we need to depict the possible outcomes at each stage. In this case, the first stage represents the first marble being drawn, and the second stage represents the second marble being drawn without replacement.
The outcome tree would look like this:
1st Stage
/ | \
W R B
/ \ /
W R B
/ \ \
W R B
The branches from the first stage represent the different possibilities for the first marble drawn: W stands for white, R for red, and B for blue.
b. To convert the outcome tree into a probability tree diagram, we need to assign probabilities to each branch. The probabilities will be based on the number of marbles of each color in the bag.
Since there are 9 marbles in total, the probability of drawing a white marble in the first stage would be 4/9, the probability of drawing a red marble would be 3/9, and the probability of drawing a blue marble would be 2/9.
The probability tree diagram would look like this:
1st Stage
/ 4/9 \
W | B
/ 4/8 3/8 |
W R B
c. To determine the probability of each outcome using the multiplicative property, you multiply the probabilities along each branch. For example, the probability of drawing a white marble followed by a white marble would be (4/9) * (3/8), which equals 12/72 or 1/6.
Similarly, the probability of drawing a red marble followed by a white marble would be (3/9) * (4/8), which simplifies to 12/72 or 1/6 as well.
You can repeat this process for all the possible outcomes to find their respective probabilities.
d. To find the probability of getting a red and a white marble using the additive property, you need to consider the different possible ways this can occur. In this case, there are two possibilities: red-white and white-red.
Using the additive property, you add the probabilities of these two outcomes together. So the probability of getting a red and a white marble would be (3/9) * (4/8) + (4/9) * (3/8), which simplifies to 12/72 + 12/72 = 24/72 or 1/3.
I hope this explanation clarifies the concept of outcome trees, probability tree diagrams, and how to calculate probabilities using the multiplicative and additive properties for you! Let me know if you have any further questions.