Find the odds of each of the following events.
(a)an event E with ​Pr(E)=2/9
(b)an event E with ​Pr(E)equals=0.40

The **odds** of an event are defined as the ratio of the probability that the event occurs to the probability that it does not occur. If \( P(E) \) is the probability of the event occurring, then the odds of the event \( E \) are given by the formula:

\[
\text{Odds of } E = \frac{P(E)}{1 - P(E)}
\]

Let's calculate the odds for both events:

### (a) Event \( E \) with \( P(E) = \frac{2}{9} \)
\[
\text{Odds of } E = \frac{\frac{2}{9}}{1 - \frac{2}{9}} = \frac{\frac{2}{9}}{\frac{7}{9}} = \frac{2}{7}
\]
So, the odds of event \( E \) are \( 2:7 \).

### (b) Event \( E \) with \( P(E) = 0.40 \)
\[
\text{Odds of } E = \frac{0.40}{1 - 0.40} = \frac{0.40}{0.60} = \frac{2}{3}
\]
So, the odds of event \( E \) are \( 2:3 \).

### Summary:
- (a) The odds of event \( E \) with \( P(E) = \frac{2}{9} \) are \( 2:7 \).
- (b) The odds of event \( E \) with \( P(E) = 0.40 \) are \( 2:3 \).

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How would you calculate the odds if the probability of an event is \( \frac{1}{3} \)?
2. What is the relationship between odds and probability?
3. How would the odds change if \( P(E) = 0.75 \)?
4. How do the odds differ when \( P(E) = 0.5 \)?
5. Can odds be greater than 1? What does it mean when they are?

**Tip:** Odds greater than 1 indicate that the event is more likely to occur than not.

Find the odds of each of the following events.
(a)an event E with ​Pr(E)=2/9
(b)an event E with ​Pr(E)=0.40

Learn how to calculate the odds of events based on their probabilities. In this problem, the odds are computed for an event E with Pr(E) = 2/9 and another event with Pr(E) = 0.40. A step-by-step solution is provided, making it easy for students to understand probability and odds. Suitable for Grades 9-12.

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