Geometry

Question Analysis
This question involves calculating the probability of mutually exclusive events within the context of fruit selection at a stand.
The main focus is on recognizing that a fruit cannot be both an apple and a banana at the same time, making these two events mutually exclusive, and applying the addition rule for mutually exclusive events, , to find the probability of selecting either an apple or a banana.

Key Concept Explanation
Mutually exclusive events imply that the occurrence of one event prevents the occurrence of the other.
In the case of fruit selection, an apple and a banana are distinct categories with no overlap.
For mutually exclusive events (selecting an apple) and (selecting a banana), the probability of either event happening is the sum of their individual probabilities, as .

Step - by - Step Solution
First, identify the number of favorable outcomes for each event and the total number of outcomes.
The total number of fruits at the stand is 50, which is the total number of possible outcomes when selecting a fruit.
Calculate the probability of event (selecting an apple). There are 20 apples, so .
Calculate the probability of event (selecting a banana). There are 15 bananas, so

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