A basket contains 9 apples, 8 bananas and 7 oranges. A fruit is picked from the basket, find the probability that it is neither an apple nor an orange.

1. Analyze the question

We are given a basket with a specific number of fruits. We need to find the probability of picking a fruit that is neither an apple nor an orange. This means we are looking for the probability of picking a banana.

2. Explain the concept

Probability is defined as:

In this case:

• Total outcomes = Total number of fruits in the basket.
• Required outcomes = Number of fruits that are neither apples nor oranges (which, in this basket, are the bananas).

3. Show the solution

Step 1: Calculate the total number of fruits. Total = (Number of apples) + (Number of bananas) + (Number of oranges) Total = 9 + 8 + 7 = 24

Step 2: Identify the "required" fruits. The question asks for fruits that are neither apples nor oranges. Since the only other fruit in the basket is the banana, the number of required fruits is the number of bananas. Number of bananas = 8

Step 3: Calculate the probability.

Step 4: Simplify the fraction. Divide both the numerator and the denominator by their greatest common divisor, which is 8:

4. Identify the answer

Comparing our result to the given options, the correct choice is B.

5. Tip

When a question asks for "neither X nor Y," it is often easier to identify the remaining category (in this case, bananas) rather than calculating the probability of X and Y separately and subtracting from 1. Always check if the "neither/nor" condition leaves you with a single category!