Two events A and B have probabilities: ﻿P left parenthesis A right parenthesis equals 0.36 comma space P left parenthesis B right parenthesis equals space 0.45 comma space P left parenthesis A intersection B right parenthesis space equals space 0.06.
What are the odds in favor of event A?

To find the odds in favor of event \( A \), we use the following formula:

\[
\text{Odds in favor of } A = \frac{P(A)}{1 - P(A)}
\]

### Given:
- \( P(A) = 0.36 \)

Now, let's calculate the odds:

\[
\text{Odds in favor of } A = \frac{0.36}{1 - 0.36} = \frac{0.36}{0.64}
\]

Simplifying the fraction:

\[
\frac{0.36}{0.64} = 0.5625
\]

Therefore, the odds in favor of event \( A \) are \( 0.5625 \) or \( \frac{9}{16} \) when expressed as a ratio. This can be interpreted as the odds being 9 to 16 in favor of event \( A \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What are the odds against event \( A \)?
2. How do you calculate the probability of event \( A \cup B \) (union of \( A \) and \( B \))?
3. What is the probability that neither \( A \) nor \( B \) happens?
4. How are the odds in favor of an event different from the event's probability?
5. If the events \( A \) and \( B \) are independent, what does \( P(A \cap B) \) become?

**Tip:** Odds represent the ratio of favorable to unfavorable outcomes, while probability focuses on favorable outcomes relative to the total possible outcomes.

Two events A and B have probabilities: ﻿P(A) = 0.36, P(B) = 0.45, P(A ∩ B) = 0.06. What are the odds in favor of event A?

Learn how to calculate the odds in favor of event A when P(A) = 0.36. This problem involves understanding probability concepts and the formula for calculating odds. Ideal for students in Grades 9-11.

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