You spin the pointers of 2 spinners, each of which is divided into 5 equal sectors numbered 1 to 5.
a) Create a tree diagram to show all the possible outcomes.
b) How many outcomes have a sum of the 2 numbers greater than or equal to 8?
You may want to draw your tree diagram on a sheet of paper, then take a picture of your diagram and attach it to this question.
HELP
Each spinner is divided into 5 equal sectors. (Two separate spinners) The pointer in each spinner, when spun, is equally likely to rest in any one of the 5 sectors. The pointer in each spinner is spun once. List the sample space and find the probability that the sum of both scores
To create a tree diagram, we can start by listing all the possible outcomes for each spinner and then combining them to show all the possible combinations.
Let's start with spinner 1, which has the numbers 1 to 5.
Spinner 1 outcomes: 1, 2, 3, 4, 5
Now, let's move on to spinner 2, which also has the numbers 1 to 5.
Spinner 2 outcomes: 1, 2, 3, 4, 5
To create the tree diagram, we will list all the possible outcomes by combining the numbers from spinner 1 with the numbers from spinner 2.
Here is the tree diagram:
```
1 2 3 4 5
/ \ / \ / \ / \ / \
1 2 1 2 1 2 1 2 1 2
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \
1...5 1...5 1...5 1...5 1...5 1...5 1...5
```
Each branch represents a possible outcome by combining the numbers from spinner 1 and spinner 2.
Now let's move on to part b of the question, which asks how many outcomes have a sum of the two numbers greater than or equal to 8.
To find the outcomes that meet this condition, we can look at the tree diagram and count the number of branches where the sum of the two numbers is greater than or equal to 8.
From the tree diagram, we can see that there are 10 outcomes where the sum is greater than or equal to 8.
Therefore, the answer to part b is 10 outcomes.
To create a tree diagram for this problem, we first start by listing all the possible outcomes for the first spinner. Since it is divided into 5 equal sectors numbered 1 to 5, the possible outcomes are 1, 2, 3, 4, and 5.
Next, we list all the possible outcomes for the second spinner. Again, since it is also divided into 5 equal sectors numbered 1 to 5, the possible outcomes are 1, 2, 3, 4, and 5.
To create the tree diagram, we start by listing the outcomes for the first spinner on the left side of the diagram, and then connect each outcome to all the possible outcomes for the second spinner. Here is an example of a tree diagram:
Spinner 1
/ | | | \
/ | | | \
1 2 3 4 5
/|\ /|\ /|\ /|\ /|\
/ | \ / | \ / | \ / | \ / | \
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
In this tree diagram, each branch represents a possible outcome of spinning both spinners. For example, the top-left branch represents the outcome of spinning the first spinner and getting a 1, and then spinning the second spinner and getting a 1. The bottom-right branch represents the outcome of spinning the first spinner and getting a 5, and then spinning the second spinner and getting a 5.
Now, to determine the number of outcomes that have a sum of the two numbers greater than or equal to 8, we can simply count the number of branches that satisfy this condition.
In the tree diagram provided, the outcome pairs with a sum greater than or equal to 8 are:
- 3 and 5
- 4 and 4
- 4 and 5
- 5 and 3
- 5 and 4
- 5 and 5
So there are 6 outcomes in total that have a sum of the two numbers greater than or equal to 8.
I hope this helps!