Exam-Style Question on Probability Distribution

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

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Question id: 430. This question is similar to one that appeared on an IB AA Standard paper in 2019. The use of a calculator is allowed.

Amelia selects a disc from a bag containing 5 green discs, 4 blue discs and 3 red discs.

She wins £1 for a green disc, £3 for a blue disc, and £7 for a red disk. The game costs £4 to play.

(a) Calculate Amelia's expected gain for this game, and hence show that the game is not fair.

After a while, $$n$$ red discs are added and Amelia wins £5 if she selects one. The game is now fair.

(b) Create an equation to represent this information.

(c) Hence, calculate the value of $$n$$.

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