Questions: Pablo is watching his favorite soccer team playing a match. The odds against his favorite team winning are 17/5. What is the probability of his favorite team winning?

Solution Steps

To find the probability of Pablo's favorite team winning, we need to convert the given odds against winning into a probability. The odds against winning are given as a ratio of unfavorable outcomes to favorable outcomes. The probability of winning is the ratio of favorable outcomes to the total number of outcomes (favorable plus unfavorable).

The odds against winning are given as \(\frac{17}{5}\). This means for every 17 unfavorable outcomes, there are 5 favorable outcomes.

The probability of winning is calculated using the formula: \[ P(\text{winning}) = \frac{1}{1 + \text{odds against winning}} \] Substituting the given odds: \[ P(\text{winning}) = \frac{1}{1 + \frac{17}{5}} = \frac{1}{1 + 3.4} = \frac{1}{4.4} \]

Simplifying the expression: \[ P(\text{winning}) = \frac{1}{4.4} \approx 0.2273 \]

Final Answer