https://file.aiquickdraw.com/mathbot/file/17285935430260a1dgzqy.jpg

Let's go through the problem step-by-step:

### a) Drawing the Sample Space Diagram

The two spinners have the following sections:
- **Spinner 1** (on the left) has 4 numbers: 3, 4, 5, 6.
- **Spinner 2** (on the right) has 3 numbers: 4, 5, 5.

Each number on Spinner 1 can be paired with each number on Spinner 2. Therefore, the sample space is the set of all possible outcomes when both spinners are spun.

The sample space diagram will be a list of ordered pairs (Spinner 1 result, Spinner 2 result):

\[
\text{Sample Space} = \{(3, 4), (3, 5), (3, 5), (4, 4), (4, 5), (4, 5), (5, 4), (5, 5), (5, 5), (6, 4), (6, 5), (6, 5)\}
\]

There are 12 total possible outcomes.

### b) Probability that at least one spinner lands on 5

To find the probability that at least one of the spinners lands on 5, we count how many outcomes have at least one 5. 

Let's list the outcomes where at least one spinner shows a 5:
- (3, 5)
- (3, 5)
- (4, 5)
- (4, 5)
- (5, 4)
- (5, 5)
- (5, 5)
- (6, 5)
- (6, 5)

There are 9 outcomes where at least one spinner shows a 5.

So, the probability of at least one 5 is:

\[
P(\text{at least one 5}) = \frac{9}{12} = \frac{3}{4}
\]

### Final Answers:
- **a)** The sample space is \(\{(3, 4), (3, 5), (3, 5), (4, 4), (4, 5), (4, 5), (5, 4), (5, 5), (5, 5), (6, 4), (6, 5), (6, 5)\}\).
- **b)** The probability that at least one spinner lands on 5 is \(\frac{3}{4}\).

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Do you have any questions or want more details?  
Here are some related questions to consider:

1. What is the probability that both spinners land on 5?
2. How would the probability change if the sections on each spinner had different probabilities?
3. What is the probability that both spinners land on the same number?
4. How would the probability change if the first spinner had 5 sections instead of 4?
5. Can you calculate the probability that neither spinner lands on 5?

**Tip**: When calculating probabilities involving "at least" one event, sometimes it's easier to calculate the probability that the event does *not* happen and subtract from 1.

The diagram shows two fair spinners. a) Draw a sample space diagram to show all the possible outcomes of spinning both of the spinners. b) What is the probability that at least one spinner lands on 5? Give your answer as a fraction in its simplest form.

Solve a probability problem involving two fair spinners with 4 and 3 sections. Learn how to create a sample space diagram and calculate the probability of at least one spinner landing on the number 5. This problem is suitable for Grades 5-7.

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