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Probability from decimal odds

Market makingEasy

A bookmaker offers decimal odds of $4$ on a team to win, meaning a winning bet of $1$ returns $4$ in total. Ignoring the bookmaker's margin, what is the implied probability that the team wins?

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Hint

Implied probability is the reciprocal of the decimal odds.

Solution

A fair bet at decimal odds of $4$ has an expected return of $4 \times p = 1$ .
So the implied probability is one divided by the odds.
The probability is $\frac{1}{4}$ .

Answer: $\frac{1}{4}$

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