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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)

1 answer

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

Step 1: Determine the Total Number of Fruits

First, we need to calculate the total number of pieces of fruit in the basket:

  • Number of apples = 20
  • Number of watermelon slices = 4
  • Number of oranges = 12

Total number of fruits = Number of apples + Number of watermelon slices + Number of oranges
Total number of fruits = 20 + 4 + 12 = 36

Step 2: Determine the Number of Favorable Outcomes

Next, we find the number of favorable outcomes, which in this case is the total number of apples and oranges.

  • Number of apples = 20
  • Number of oranges = 12

Total number of favorable outcomes = Number of apples + Number of oranges
Total number of favorable outcomes = 20 + 12 = 32

Step 3: Calculate the Probability

Probability is calculated as the number of favorable outcomes divided by the total number of outcomes. Thus, the probability of selecting an apple or an orange is:

\[ P(\text{apple or orange}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Substituting in the values:

\[ P(\text{apple or orange}) = \frac{32}{36} \]

Step 4: Simplify the Fraction

To simplify \(\frac{32}{36}\):

Both the numerator and the denominator can be divided by 4:

\[ \frac{32 \div 4}{36 \div 4} = \frac{8}{9} \]

Thus, the probability of selecting an apple or an orange is:

\[ P(\text{apple or orange}) = \frac{32}{36} = \frac{8}{9} \]

Summary of Responses

Based on the options provided in Part 1, the probability can be stated as:

32/36 (the first option)

Explanation of the Process

  1. Identify Total Fruits: We first counted all types of fruits to find the total.
  2. Identify Favorable Outcomes: We added apples and oranges as they were our favorable outcomes.
  3. Calculate Probability: We divided the number of favorable outcomes by the total number of fruits to find the required probability.
  4. Simplification: Lastly, I simplified the fraction to provide the most accurate and simplified form of the probability.

With this clear and structured approach, we can confidently represent our answer and ensure we grasp the concept of probability through addition of outcomes and division for normalization.