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Question 1

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?(2 points)
Responses

3236
32 over 36

2036
20 over 36

1236
12 over 36

1636
16 over 36
Question 2
Part 2: Explain the process you used to solve this problem. Show your work and explain using math vocabulary. (2 points)
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1 answer

Question 1

To find the probability of selecting an apple or an orange from the basket of fruits, follow these steps:

  1. Count the Total Number of Fruits:

    • Apples: 20
    • Watermelon slices: 4
    • Oranges: 12

    Therefore, the total number of fruits in the basket is: \[ \text{Total Fruits} = 20 \text{ (apples)} + 4 \text{ (watermelon slices)} + 12 \text{ (oranges)} = 36 \]

  2. Count the Number of Favorable Outcomes: To find the number of favorable outcomes for selecting an apple or an orange, add the number of apples and oranges: \[ \text{Favorable Outcomes} = 20 \text{ (apples)} + 12 \text{ (oranges)} = 32 \]

  3. Calculate the Probability: Probability is calculated using the formula: \[ P(A \text{ or } O) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} \] Substituting the values: \[ P(A \text{ or } O) = \frac{32}{36} \]

    This fraction can be simplified: \[ P(A \text{ or } O) = \frac{8}{9} \quad \text{(not asked, but shown for clarity)} \]

Responses to Question 1

The probability of selecting an apple or an orange is 32 over 36.

Question 2

Explanation of the Process

To calculate the probability of selecting either an apple or an orange from a basket of fruits, I first determined the total number of fruits present, which is essential for understanding the sample space.

  • Step 1: I summed up the total count of each type of fruit in the basket, which includes 20 apples, 4 watermelon slices, and 12 oranges. This gave me a total of 36 pieces of fruit.

  • Step 2: I identified the favorable outcomes for my event of interest, which is to select either an apple or an orange. By adding the number of apples (20) and oranges (12), I got 32 favorable outcomes.

  • Step 3: Finally, I used the probability formula, which is the ratio of the number of favorable outcomes to the total outcomes. In this case, it was \( \frac{32}{36} \). This process ensures that I accounted for both the desired outcomes and the total possibilities in the selection process. Hence, I arrived at the final answer: the probability of selecting an apple or an orange from the basket is \( \frac{32}{36} \).