Question

find the odds of each of the following events.
(a) an event e with pr(e) = 6/7
(b) an event e with pr(e) = 0.6

(a) the odds are □ to □
(simplify your answer.)

Explanation:

Step1: Recall the odds formula

The formula for odds in favor of an event \( E \) is \( \text{Odds}(E)=\frac{\text{Pr}(E)}{1 - \text{Pr}(E)} \). For part (a), we know \( \text{Pr}(E)=\frac{6}{7} \), so first find \( 1-\text{Pr}(E) \).
\( 1-\frac{6}{7}=\frac{7 - 6}{7}=\frac{1}{7} \)

Step2: Calculate the odds

Now, use the odds formula: \( \text{Odds}(E)=\frac{\frac{6}{7}}{\frac{1}{7}} \). When dividing fractions, we multiply by the reciprocal, so \( \frac{6}{7}\times\frac{7}{1} = 6 \). So the odds are \( 6 \) to \( 1 \).

Answer:

6 to 1