The spinner is divided into equal parts. Use a tree diagram to find the probability that the spinner will land on a constant both times if the spinner is spun twice.
google tree diagrams
To find the probability that the spinner will land on a constant both times if the spinner is spun twice, we can create a tree diagram.
Let's assume the spinner has 6 equal parts labeled with numbers from 1 to 6.
Step 1: Draw a horizontal line to represent the first spin of the spinner.
Step 2: Label each branch with the possible outcomes of the first spin, which are numbers 1 to 6.
Step 3: Draw another horizontal line below each branch of the first spin to represent the second spin of the spinner.
Step 4: Label each branch of the second spin with the possible outcomes, which are numbers 1 to 6.
Step 5: Count the number of branches where the outcome is the same constant for both spins.
Step 6: Calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes.
Here is a tree diagram that shows the possible outcomes:
1
/ \
/ \
/ \
/ \
/ \
/ \
/ \
1 2
/ \ / \
/ \ / \
/ \ / \
1 2 1 3
/ \ / \ / \ / \
/ \ / \ / \ / \
1 2 1 3 1 2 1 4
/ \ / \ /\ / \ / \ / \
1 2 2 3 / \/ \ 2 3 1 5
... ...
Continue the tree diagram until you have all possible outcomes for both spins.
In this case, there are 36 branches representing all the possible outcomes of the two spins.
Count the number of branches where the outcome is the same constant for both spins. For example, when the first spin is 1, there are 6 branches where the second spin is also 1.
Sum up all the branches where the outcome is the same constant for both spins.
In this case, there are 6 branches for each constant from 1 to 6, so the total number of favorable outcomes is 6 x 6 = 36.
Finally, the probability is calculated by dividing the number of favorable outcomes (36) by the total number of possible outcomes (36), which gives us 36/36 = 1.
Therefore, the probability that the spinner will land on a constant both times if the spinner is spun twice is 1.
To solve this problem, we can use a tree diagram to represent the possible outcomes of spinning the spinner twice.
Here's how you can construct the tree diagram:
1. Start with a single branch representing the first spin. Since the spinner is divided into equal parts, each branch will represent a different outcome of the first spin with an equal probability.
2. For each outcome of the first spin, create two branches to represent the second spin. Again, each branch will represent a different outcome of the second spin with an equal probability.
3. Continue this process until you have accounted for all possible outcomes of the second spin for each outcome of the first spin.
4. Label each final branch with the corresponding outcomes of both spins.
For example, let's say the spinner has 4 equal parts labeled A, B, C, and D. The tree diagram will look as follows:
_________
| |
A | |
| |
|_________|
/ \
/ \
_______/____ ____\________
| | | |
A | | B | |
| | | |
|_____________| |_____________|
/ \ / \
/ \ / \
_______/____ ____\____ ____/____ ______\____
| | | || | |
A | |B | || C |D |
| | | || | |
|____________| |__________||____________|___________|
Now, let's count the favorable outcomes, i.e., the branches where the spinner lands on a constant both times. In this case, there are 2 favorable outcomes: (A, A) and (B, B).
Finally, we calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, since we have 4 possible outcomes for each spin, the total number of outcomes for 2 spins is 4 x 4 = 16.
So the probability of the spinner landing on a constant both times is 2/16 = 1/8.