# 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: 365. This question is similar to one that appeared on an IB Standard paper in 2014. The use of a calculator is not allowed.

A game at a fayre consists of a players throwing one dart at the board pictured below.

The probability of hitting each region and the points scored for hitting that region is given in this table.

RegionProbabilityPoints
A$$\frac{1}{25}$$50
B$$\frac{2}{25}$$$$x$$
C$$\frac{4}{25}$$20
D$$\frac{5}{25}$$10

(a) Find the probability that the dart does not hit the board.

The player scores points as shown in the table above but they lose 20 points if they miss the board completely.

(b) Given that the game is a fair game, find the value of $$x$$, the number of points awarded for hitting the B region of the board.

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