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.(1 point)
Responses
9
9
24
24
27
27
81
81
There are 3 possible outcomes each time the spinner is spun, so we have 3 branches coming from each spin. To determine the total number of outcomes after three spins, we multiply the number of outcomes at each spin together.
Using a tree diagram:
1st spin:
- 1, 2, 3
2nd spin:
- 1, 2, 3 for each outcome of the 1st spin
- (1, 1), (1, 2), (1, 3)
- (2, 1), (2, 2), (2, 3)
- (3, 1), (3, 2), (3, 3)
3rd spin:
- 1, 2, 3 for each outcome of the 2nd spin
- (1, 1, 1), (1, 1, 2), (1, 1, 3)
- (1, 2, 1), (1, 2, 2), (1, 2, 3)
- ...
- (3, 2, 1), (3, 2, 2), (3, 2, 3)
- (3, 3, 1), (3, 3, 2), (3, 3, 3)
Counting all outcomes, we have 3^3 = 27 possible outcomes.
Therefore, the correct response is: 27