Use a tree diagram or a table to determine how many possible outcomes there are when a spinner that has three equal parts labeled 1,2, and 3 is spun three times.
To determine the total number of possible outcomes when spinning a three-part spinner three times, we can use a tree diagram.
On the first spin, there are three possible outcomes: 1, 2, or 3.
On the second spin, there are three possible outcomes for each outcome of the first spin, resulting in a total of 3 x 3 = 9 possible outcomes.
On the third spin, there are three possible outcomes for each outcome of the second spin, resulting in a total of 9 x 3 = 27 possible outcomes.
Therefore, there are 27 possible outcomes when a three-part spinner is spun three times.
Alternatively, we can also represent the possible outcomes in a table:
1st Spin | 2nd Spin | 3rd Spin
1 1 1
2 1 1
3 1 1
1 2 1
2 2 1
3 2 1
1 3 1
2 3 1
3 3 1
1 1 2
2 1 2
3 1 2
1 2 2
2 2 2
3 2 2
1 3 2
2 3 2
3 3 2
1 1 3
2 1 3
3 1 3
1 2 3
2 2 3
3 2 3
1 3 3
2 3 3
3 3 3
There are a total of 27 possible outcomes listed in the table, confirming our previous result.