To solve the problem of finding the probability that the sum of the numbers from two fair spinners, A and B, is 5 or less, follow these steps:
### Step 1: List the Sections on Each Spinner
- Spinner A: [1, 2, 3, 4]
- Spinner B: [2, 3, 4, 5]
### Step 2: Determine the Total Number of Possible Outcomes
Each spinner has 4 sections, so when both spinners are spun, the total number of possible outcomes is [tex]\(4 \times 4 = 16\)[/tex].
### Step 3: List the Successful Outcomes
We need to identify the outcomes where the sum of the numbers from both spinners is 5 or less. We'll list combinations from both spinners that satisfy this condition.
- From Spinner A (1):
- For b = 2: [tex]\(1 + 2 = 3\)[/tex]
- For b = 3: [tex]\(1 + 3 = 4\)[/tex]
- For b = 4: [tex]\(1 + 4 = 5\)[/tex]
- From Spinner A (2):
- For b = 2: [tex]\(2 + 2 = 4\)[/tex]
- For b = 3: [tex]\(2 + 3 = 5\)[/tex]
- From Spinner A (3):
- For b = 2: [tex]\(3 + 2 = 5\)[/tex]
- From Spinner A (4):
- None, as all sums exceed 5
Let's count these successful outcomes:
1. [tex]\((1, 2)\)[/tex]
2. [tex]\((1, 3)\)[/tex]
3. [tex]\((1, 4)\)[/tex]
4. [tex]\((2, 2)\)[/tex]
5. [tex]\((2, 3)\)[/tex]
6. [tex]\((3, 2)\)[/tex]
Thus, there are 6 successful outcomes.
### Step 4: Calculate the Probability
The probability of an event is given by the ratio of the number of successful outcomes to the total number of possible outcomes.
[tex]\[
\text{Probability} = \frac{\text{Number of Successful Outcomes}}{\text{Total Number of Possible Outcomes}} = \frac{6}{16}
\][/tex]
### Step 5: Simplify the Fraction
Simplifying [tex]\(\frac{6}{16}\)[/tex]:
[tex]\[
\frac{6}{16} = \frac{3}{8}
\][/tex]
Therefore, the probability that the total is 5 or less is [tex]\(\frac{3}{8}\)[/tex].
