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Probability from a favorite line

Market makingEasy

A favorite is quoted at a moneyline of $- 150$ , meaning a bettor must stake $150$ to win a profit of $100$ . Ignoring any margin, what is the implied probability that the favorite wins?

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Hint

Compare the stake to the total return.

Solution

Staking $150$ returns $150 + 100 = 250$ in total if the bet wins.
The implied probability is the stake divided by the total return.
The probability is $\frac{150}{250} = \frac{3}{5}$ .

Answer: $\frac{3}{5}$

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