JAMB 2025 Mathematics · Question 34

In a basket of fruits, there are 6 grapes, 11 bananas, and 13 oranges. If one fruit is chosen at random, what…

Question

In a basket of fruits, there are 6 grapes, 11 bananas, and 13 oranges. If one fruit is chosen at random, what is the probability that the fruit is either a grape or a banana?

A. $\frac{17}{30}$
B. $\frac{11}{30}$
C. $\frac{6}{30}$
D. $\frac{5}{30}$

Answer: A. $\frac{17}{30}$

Explanation written with AI and checked against the answer key

1. Analyze the question

We are asked to find the probability of picking either a grape or a banana from a basket containing a specific number of different fruits.

2. Explain the concept

Probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes:

\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}

When we want to find the probability of one event or another event occurring (and they are mutually exclusive, meaning you can't pick a fruit that is both a grape and a banana at the same time), we add their individual probabilities together.

3. Show the solution

Step 1: Find the total number of fruits in the basket.

\text{Total} = \text{Grapes} + \text{Bananas} + \text{Oranges}

\text{Total} = 6 + 11 + 13 = 30

Step 2: Find the number of favorable outcomes. We want either a grape or a banana.

\text{Favorable outcomes} = \text{Number of grapes} + \text{Number of bananas}

\text{Favorable outcomes} = 6 + 11 = 17

Step 3: Calculate the probability.

\text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}}

\text{Probability} = \frac{17}{30}

4. Identify the answer

Comparing our result to the options provided: A. $\frac{17}{30}$ B. $\frac{11}{30}$ C. $\frac{6}{30}$ D. $\frac{5}{30}$

The correct option is A.

5. Tip

In probability questions involving "OR," always think of addition. If the question had asked for the probability of picking a fruit that is "neither a grape nor a banana," you would simply subtract the probability of picking a grape or banana from 1 (the total probability).

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