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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 32/36 32 over 36 20/36 20 over 36 12/36 12 over 36 16/36 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

Part 1: Calculating the Probability

First, let's calculate the total number of fruits in the basket:

  • Number of apples = 20
  • Number of watermelons = 4
  • Number of oranges = 12

To find the total number of fruits, we add these quantities together:

\[ \text{Total fruits} = 20 + 4 + 12 = 36 \]

Next, we want to find the probability of selecting either an apple or an orange. Therefore, we need to add the number of apples and oranges together:

\[ \text{Number of apples or oranges} = 20 + 12 = 32 \]

Now, the probability \( P \) of selecting an apple or an orange is the number of favorable outcomes (selecting an apple or an orange) divided by the total number of outcomes (total fruits).

\[ P(\text{apple or orange}) = \frac{\text{Number of apples or oranges}}{\text{Total fruits}} = \frac{32}{36} \]

Now, we can simplify this fraction:

\[ P(\text{apple or orange}) = \frac{32 \div 4}{36 \div 4} = \frac{8}{9} \]

Answer:

The probability of selecting an apple or an orange is \( \frac{32}{36} \).

Part 2: Explanation of the Process

To solve the problem, I followed these steps:

  1. Identifying the Parts: I began by identifying how many of each type of fruit there were in the basket (apples, watermelons, and oranges).

  2. Calculating the Total: I determined the total number of fruits by summing the quantities of each type of fruit. This total is essential because the probability is always calculated by comparing the number of favorable outcomes to the total number of possible outcomes.

  3. Counting Favorable Outcomes: I then counted the number of favorable outcomes for the event we are interested in, which is selecting either an apple or an orange. This involved adding the number of apples and oranges.

  4. Calculating the Probability: Finally, I calculated the probability by taking the ratio of the number of favorable outcomes (apples and oranges combined) to the total number of fruits. This is a fundamental concept in probability, where the probability of an event is defined as the number of successful outcomes divided by the total number of outcomes.

In summary, the process involved determining totals, counting, and creating a ratio to represent the likelihood of selecting an apple or an orange. By using clear mathematical operations and definitions, I was able to arrive at the solution effectively.