# 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: 268. This question is similar to one that appeared on a GCSE Higher paper (specimen) for 2017. The use of a calculator is allowed.

At the Trantown annual Fayre there are a number of different sideshows designed to raise money for cancer research. Roger is looking after two of these, the lucky dip and the raffle.

(a) At the lucky dip it costs £1 to enter and everyone wins one of three different types of prize.

• The probability of winning a teddy bear is $$x$$;
• The probability of winning is soft drink is $$2x$$;
• The probability of winning chocolate bar is $$7x$$.

Calculate the value of $$x$$.

(b) Roger is offering a free raffle ticket for every raffle ticket purchased. He tells people that this doubles their chances of winning. Is he correct?

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