you spin two spinners, each of which is divided into five congruent sections numbered 1 to 5. list all possible outcomes. then find the probability of getting the same number on both spins
so, list them all:
1,1
1,2
...
5,4
5,5
Now -- how many of them have matching spins?
17422
To list all possible outcomes, we can simply list all the combinations of the numbers on both spinners:
Spinner 1: 1, 2, 3, 4, 5
Spinner 2: 1, 2, 3, 4, 5
All possible outcomes:
1-1, 1-2, 1-3, 1-4, 1-5
2-1, 2-2, 2-3, 2-4, 2-5
3-1, 3-2, 3-3, 3-4, 3-5
4-1, 4-2, 4-3, 4-4, 4-5
5-1, 5-2, 5-3, 5-4, 5-5
There are a total of 25 possible outcomes.
To find the probability of getting the same number on both spins, we need to determine the number of favorable outcomes (where both spins yield the same number) and divide it by the total number of possible outcomes.
In this case, there are 5 favorable outcomes: 1-1, 2-2, 3-3, 4-4, 5-5.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 5 / 25
Probability = 1/5
Probability = 0.2 (or 20%)
So, the probability of getting the same number on both spins is 0.2 or 20%.
To list all the possible outcomes when spinning two spinners, we need to consider the numbers on each spinner and the combinations of these numbers.
Spinner 1 outcomes: 1, 2, 3, 4, 5
Spinner 2 outcomes: 1, 2, 3, 4, 5
Now, let's find the possible outcomes by combining the numbers from both spinners:
1 from Spinner 1 with 1 from Spinner 2
1 from Spinner 1 with 2 from Spinner 2
1 from Spinner 1 with 3 from Spinner 2
1 from Spinner 1 with 4 from Spinner 2
1 from Spinner 1 with 5 from Spinner 2
2 from Spinner 1 with 1 from Spinner 2
2 from Spinner 1 with 2 from Spinner 2
2 from Spinner 1 with 3 from Spinner 2
2 from Spinner 1 with 4 from Spinner 2
2 from Spinner 1 with 5 from Spinner 2
3 from Spinner 1 with 1 from Spinner 2
3 from Spinner 1 with 2 from Spinner 2
3 from Spinner 1 with 3 from Spinner 2
3 from Spinner 1 with 4 from Spinner 2
3 from Spinner 1 with 5 from Spinner 2
4 from Spinner 1 with 1 from Spinner 2
4 from Spinner 1 with 2 from Spinner 2
4 from Spinner 1 with 3 from Spinner 2
4 from Spinner 1 with 4 from Spinner 2
4 from Spinner 1 with 5 from Spinner 2
5 from Spinner 1 with 1 from Spinner 2
5 from Spinner 1 with 2 from Spinner 2
5 from Spinner 1 with 3 from Spinner 2
5 from Spinner 1 with 4 from Spinner 2
5 from Spinner 1 with 5 from Spinner 2
There are a total of 25 possible outcomes.
To find the probability of getting the same number on both spins, we need to determine the number of favorable outcomes (where the number is the same) and divide it by the total number of possible outcomes.
From the list above, we can see that there are 5 favorable outcomes (1/1, 2/2, 3/3, 4/4, 5/5) where the numbers are the same.
Therefore, the probability of getting the same number on both spins is 5/25 or simplified, 1/5.