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Match outcome market

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A match has exactly $3$ outcomes: home win, draw and away win, with decimal odds of $1.6$ , $4$ and $6$ . After scaling the raw implied probabilities proportionally to sum to $1$ , what is the probability that the home team does not lose (home win or draw)? Give an exact fraction.

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Hint

Scale by the sum of the raw implied probabilities.

Solution

The raw probabilities are $\frac{5}{8}$ , $\frac{1}{4}$ and $\frac{1}{6}$ , which sum to $\frac{25}{24}$ .
The raw probability of a home win or a draw is $\frac{5}{8} + \frac{1}{4} = \frac{21}{24}$ .
Scaled, it is $(\frac{21}{24}) \div (\frac{25}{24}) = \frac{21}{25}$ .

Answer: $\frac{21}{25}$

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