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Injury news

Market makingEasy

A contract pays $100$ if a team wins and $0$ otherwise, and its fair value is $40$ . News arrives that cuts the team's probability of winning to $\frac{3}{4}$ of its previous value. What is the new fair value?

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Hint

Fair value is proportional to the probability of winning.

Solution

The old probability of winning is $\frac{40}{100} = 0.4$ .
The new probability is $0.4 \times \frac{3}{4} = 0.3$ .
The new fair value is $100 \times 0.3 = 30$ .

Answer: $30$

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