Question
Part 2: Explain the process you used to solve this problem. Show your work and explain using math vocabulary.
Part 1: A basket of fruits contains 20 apples, 4 watermelon slices, and 12 oranges. If a piece of fruit is to be selected randomly from the box, what is the probability of selecting an apple or an orange?
Part 1: A basket of fruits contains 20 apples, 4 watermelon slices, and 12 oranges. If a piece of fruit is to be selected randomly from the box, what is the probability of selecting an apple or an orange?
Answers
GPT-4o mini
To find the probability of selecting an apple or an orange from the basket of fruits, we can follow these steps:
1. **Determine the total number of pieces of fruit:**
We add the number of each type of fruit in the basket.
- Number of apples = 20
- Number of watermelon slices = 4
- Number of oranges = 12
Now, we sum these values to find the total number of pieces of fruit:
\[
\text{Total number of fruits} = \text{Number of apples} + \text{Number of watermelon} + \text{Number of oranges}
\]
\[
\text{Total number of fruits} = 20 + 4 + 12 = 36
\]
2. **Calculate the number of favorable outcomes:**
We want to find the number of favorable outcomes for selecting either an apple or an orange. We add the number of apples and oranges together:
\[
\text{Number of favorable outcomes} = \text{Number of apples} + \text{Number of oranges}
\]
\[
\text{Number of favorable outcomes} = 20 + 12 = 32
\]
3. **Compute the probability:**
The probability of selecting an apple or an orange is given by the formula:
\[
P(\text{apple or orange}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of fruits}}
\]
Now, we can substitute the values we calculated:
\[
P(\text{apple or orange}) = \frac{32}{36}
\]
4. **Simplify the fraction:**
To simplify \(\frac{32}{36}\), we find the greatest common divisor (GCD) of 32 and 36, which is 4. We then divide both the numerator and the denominator by 4:
\[
P(\text{apple or orange}) = \frac{32 \div 4}{36 \div 4} = \frac{8}{9}
\]
5. **Final answer:**
Therefore, the probability of selecting an apple or an orange from the basket is:
\[
P(\text{apple or orange}) = \frac{8}{9}
\]
In summary, I calculated the total number of fruits, determined the favorable outcomes for selecting an apple or orange, and then used the formula for probability to find and simplify the final answer.
1. **Determine the total number of pieces of fruit:**
We add the number of each type of fruit in the basket.
- Number of apples = 20
- Number of watermelon slices = 4
- Number of oranges = 12
Now, we sum these values to find the total number of pieces of fruit:
\[
\text{Total number of fruits} = \text{Number of apples} + \text{Number of watermelon} + \text{Number of oranges}
\]
\[
\text{Total number of fruits} = 20 + 4 + 12 = 36
\]
2. **Calculate the number of favorable outcomes:**
We want to find the number of favorable outcomes for selecting either an apple or an orange. We add the number of apples and oranges together:
\[
\text{Number of favorable outcomes} = \text{Number of apples} + \text{Number of oranges}
\]
\[
\text{Number of favorable outcomes} = 20 + 12 = 32
\]
3. **Compute the probability:**
The probability of selecting an apple or an orange is given by the formula:
\[
P(\text{apple or orange}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of fruits}}
\]
Now, we can substitute the values we calculated:
\[
P(\text{apple or orange}) = \frac{32}{36}
\]
4. **Simplify the fraction:**
To simplify \(\frac{32}{36}\), we find the greatest common divisor (GCD) of 32 and 36, which is 4. We then divide both the numerator and the denominator by 4:
\[
P(\text{apple or orange}) = \frac{32 \div 4}{36 \div 4} = \frac{8}{9}
\]
5. **Final answer:**
Therefore, the probability of selecting an apple or an orange from the basket is:
\[
P(\text{apple or orange}) = \frac{8}{9}
\]
In summary, I calculated the total number of fruits, determined the favorable outcomes for selecting an apple or orange, and then used the formula for probability to find and simplify the final answer.