Geometry

Question Analysis
This question focuses on calculating the probability of two consecutive dependent events.
The main task is to accurately determine the probabilities of each draw as the composition of fruits in the basket changes after the first draw, and then correctly apply the multiplication rule for dependent events to find the combined probability of these two events.

Key Concept Explanation
Dependent events imply that the outcome of the first draw influences the probability of the second draw.
In a without - replacement scenario, when the first fruit is taken out, both the total number of fruits and the number of fruits of each type in the basket decrease, which in turn affects the probabilities for the second draw.

Step-by-Step Solution
Calculate the probability of drawing an orange on the first draw:
There are 5 oranges out of 14 total fruits, so .
Calculate the probability of drawing a banana on the second draw given that an orange was drawn on the first draw:
After removing one orange, there are 13 fruits left, and 2 of them are bananas.
So .
Use the multiplication rule for dependent events:

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