A spinner has three congruent sectors colored orange, green, and purple.
Every spin has has 1/3 chance of landing on any color and there is 1/9 chance of landing on orange and then on purple.
There is 1/3 chance of landing on same color twice in a row.
I need to make a tree diagram verifying these answers and I don't know how to do it. Any help would be appreciated. Thanks!
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
Same color twice in a row = 1/3 * 1/3
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Jimmy is rolling a number cube labeled 1-6 and also spinning a 3-section spinner labeled red, yellow, and blue.
How many outcomes are possible
What are they? make a list
what is the probability of spinning yellow?
4. If Mary says she always rolls yellow with even numbers 80% of the time is she right or wrong? How do you know
Sure! I can help you create a tree diagram for this scenario.
First, let's start with the initial spin. Since there are three congruent sectors, each color has a 1/3 chance of being landed on. We'll start by creating three branches from the initial spin, each representing a different color: orange, green, and purple.
Next, let's consider the case where the first spin lands on orange. According to the given information, there is a 1/9 chance of landing on orange and then on purple. So from the orange branch, create a smaller sub-branch showing the possibility of landing on purple after orange, with a probability of 1/9.
Now, let's consider the case where the first spin lands on green. Since there are no additional conditions or probabilities mentioned for the green color, this branch can be a simple straight line.
Finally, let's consider the case where the first spin lands on purple. Again, since there are no additional conditions or probabilities mentioned for the purple color, this branch can also be a simple straight line.
To summarize, your tree diagram should look like this:
- Initial spin (1/3)
- Orange (1/3)
- Purple (1/9)
- Green (1/3)
- Purple (1/3)
Please note that the specific probabilities mentioned above are based on the information given in your question. You can adjust the probabilities according to the exact probabilities provided in your problem if they differ from the ones mentioned here.
Sure! I can help you create a tree diagram to verify these probabilities.
To start, we need to consider the possible outcomes of the first spin. Since the spinner has three congruent sectors, each with an equal chance of being landed on, we can represent this with three branches: one for orange, one for green, and one for purple.
Next, we consider the possible outcomes of the second spin. If we landed on orange on the first spin, there is a 1/3 chance of landing on orange again, a 1/3 chance of landing on green, and a 1/3 chance of landing on purple. We can represent these outcomes with three branches extending from the orange branch. Similarly, we do the same for the green and purple branches.
Now, we need to incorporate the given probability of landing on orange and then on purple. We can represent this with an additional branch from the orange branch that leads to the purple branch. Note that the probability of landing on orange and then on purple is 1/9, so we label this branch with 1/9.
Finally, to account for the probability of landing on the same color twice in a row, we add an additional branch from each branch representing a color. These branches loop back to the same color, indicating that the spinner landed on the same color twice in a row. Since there is a 1/3 chance of this happening, we label each of these branches with 1/3.
Below is an example tree diagram that represents the given probabilities:
|
___________
| |
O G P
---|---|--- ---|---|--- ---|---|---
O G P O G P O G P
| | | | | | | | |
P G P O P P O G O
(1/9)
| |
P O
Note: O stands for orange, G stands for green, and P stands for purple.
In this tree diagram, we can see that the probability of landing on the same color twice in a row is indeed 1/3, as stated. Additionally, we can verify that there is a 1/9 chance of landing on orange and then on purple by following the corresponding path in the diagram.
I hope this helps you create your own tree diagram!