There are two spinners. Each spinner is numbered 1-4. Each spinner is spun once. Find the probability of spinning each of the following: a 3 on both spinners, 1 on one spinner and a 3 on the other, both numbers less than 4, 3 on at least one spinner.

there are only 16 possible outcomes.

I would make a chart showing all your cases and then just do a quick count for you different situations

e.g.

1,1 - 1,2 - 1,3 - 1,4
2,1 ----
..
4,1 - 4,2 - 4,3 - 4,4

To find the probability of various outcomes when spinning the two numbered spinners, we need to know the total number of possible outcomes and the number of favorable outcomes for each event.

1. Probability of spinning a 3 on both spinners:
The total number of possible outcomes for each spinner is 4 since each spinner is numbered 1 to 4. Since there are 4 possible outcomes for each spinner, the total number of possible outcomes for both spinners is 4 x 4 = 16. There is only 1 favorable outcome where both spinners show a 3: (3, 3). Therefore, the probability of spinning a 3 on both spinners is 1/16.

2. Probability of spinning a 1 on one spinner and a 3 on the other:
The total number of possible outcomes remains 16, but now we need to consider the number of favorable outcomes. Since there is 1 favorable outcome for spinning a 1 on one spinner and 1 on the other, the probability of this event occurring is 1/16.

3. Probability of both numbers being less than 4:
We need to determine the favorable outcomes for this event. Since both spinners are numbered from 1 to 4, the favorable outcomes are (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), and (3, 3), giving us a total of 9 favorable outcomes. Therefore, the probability of both numbers being less than 4 is 9/16.

4. Probability of spinning a 3 on at least one spinner:
To find this probability, we need to determine the number of favorable outcomes. Spinners can either show a 3 or not, so there are 2 outcomes for each spinner. Since we have two spinners, the total number of possible outcomes is 2 x 2 = 4. The favorable outcomes for spinning a 3 on at least one spinner are (3, 1), (3, 2), (3, 3), (1, 3), (2, 3), giving us a total of 5 favorable outcomes. Therefore, the probability of spinning a 3 on at least one spinner is 5/16.

To find the probability of each event, we first need to determine the total number of outcomes.

Since there are 4 numbers on each spinner, there are a total of 4*4 = 16 possible outcomes when both spinners are spun once.

Now, let's calculate the probability of each event step-by-step:

1. Probability of spinning a 3 on both spinners:
Since there is only 1 number '3' on each spinner, the probability of spinning a 3 on the first spinner is 1/4, and the probability of spinning a 3 on the second spinner is also 1/4.
Thus, the probability of spinning a 3 on both spinners is (1/4) * (1/4) = 1/16.

2. Probability of spinning a 1 on one spinner and a 3 on the other:
There is 1 number '1' on each spinner, so the probability of spinning a 1 on one spinner is 1/4. Similarly, the probability of spinning a 3 on the other spinner is 1/4.
Since there are two spinners, the event can occur in two ways: (1, 3) or (3, 1). Therefore, we need to add the probabilities of both cases.
So, the probability of spinning a 1 on one spinner and a 3 on the other is (1/4) * (1/4) + (1/4) * (1/4) = 2/16 = 1/8.

3. Probability of both numbers less than 4:
Since all the numbers on both spinners are less than 4, there are a total of 4*4 = 16 possible outcomes.
Therefore, the probability of both numbers being less than 4 is 16/16 = 1.

4. Probability of spinning a 3 on at least one spinner:
To calculate this probability, we need to consider all the possible outcomes where at least one spinner shows a 3: (1, 3), (2, 3), (3, 3), (4, 3), (3, 1), (3, 2), (3, 3), (3, 4).
Out of the 16 possible outcomes, 8 of them have at least one spinner showing a 3.
Therefore, the probability of spinning a 3 on at least one spinner is 8/16 = 1/2.

In summary, the probabilities are:
- Probability of spinning a 3 on both spinners: 1/16
- Probability of spinning a 1 on one spinner and a 3 on the other: 1/8
- Probability of both numbers less than 4: 1
- Probability of spinning a 3 on at least one spinner: 1/2