# Exam-Style Question on Probability

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 620. This question is similar to one that appeared on a GCSE Higher paper in 2020. The use of a calculator is allowed.

A monkey comes across a box of red and green apples in the jungle. All of the apples are the same size.

There are $$n$$ red apples in the box.

There are 9 green apples in the box.

The monkey is going to take at random an apple from the box.

The primatologist who provided the box of apples and who is observing the monkey's behaviour suspects the monkey is colour blind. He concludes that the probability that the apple will be red is $$\dfrac{3}{7}$$.

(a) Show why the probability cannot be $$\dfrac{3}{7}$$.

After the monkey has taken the first apple from the box and eaten it, he is going to take at random a second apple from the box.

(b) Given that the probability that both the apples he takes will be red is $$\dfrac{2}{5}$$ work out the number of red apples in the box.

You must show all your working.

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