https://file.aiquickdraw.com/mathbot/file/1726526845633o0zw7ept.jpg

Let's analyze and solve this problem step by step:

### Part a) What number should replace A?

The diagram shows two four-sided spinners with numbers 1, 2, 3, and 4 on each. When the results from the two spinners are added together, we get the totals shown in the table.

The value that should replace A is the sum of the two spinner results. The table represents the sums of possible results from each spinner's outcomes. Each number in the grid corresponds to the sum of one result from the left spinner and one from the top spinner.

The row with the "A" has the second number from the left (which represents a result of 3 on the left spinner), and the column where "A" is located corresponds to the third number from the top (which represents a result of 2 on the top spinner).

So, to find the value that should replace A, we add:
\[
3 \, \text{(from the left spinner)} + 2 \, \text{(from the top spinner)} = 5
\]
Thus, the value that should replace A is **5**.

---

### Part b) What is the probability of the total being 6?

We will now calculate the probability of getting a total sum of 6 when the two spinners are spun. 

First, let's identify how many possible outcomes could give a total of 6. Referring to the table, we look for the occurrences of the number 6. From the table:
- One occurrence of 6 happens when the left spinner shows 2, and the top spinner shows 4.
- Another occurrence of 6 happens when the left spinner shows 3, and the top spinner shows 3.
- One more occurrence of 6 happens when the left spinner shows 4, and the top spinner shows 2.

So, there are **3 outcomes** that result in a sum of 6.

Next, we calculate the total number of possible outcomes. Since each spinner has 4 sides, the total number of outcomes when spinning both spinners is:
\[
4 \times 4 = 16
\]

The probability of getting a total of 6 is therefore:
\[
\frac{3}{16}
\]

Thus, the probability of the total being 6 is **\(\frac{3}{16}\)**.

---

Would you like more details or have any questions on this solution? 

Here are 5 related questions you could explore:
1. What is the probability of the total being 5?
2. What is the probability of getting a total of 8?
3. How many outcomes result in a total of 7?
4. If the spinner numbers were changed to 1 through 5, how would the probabilities change?
5. What is the expected sum of the numbers from the two spinners?

**Tip:** For calculating probabilities, always count the favorable outcomes and compare them with the total number of possible outcomes!

The diagram below shows the totals from adding together the results from spinning two fair four-sided spinners. a) What number should replace A? b) What is the probability of the total being 6? Give your answer as a fraction in its simplest form.

Solve the probability problem involving two four-sided spinners. Learn how to find the sum of outcomes and calculate the probability of getting a total of 6. Suitable for students in Grades 6-8.

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