1. Suppose the odds in favour of good weather
tomorrow are 3:2.
a) What are the odds against good weather
tomorrow?
b) What is the probability of good weather
tomorrow?


The problem gives us the **odds in favor** of good weather tomorrow as 3:2. Let's break down the questions:

### a) What are the odds **against** good weather tomorrow?

If the odds **in favor** of good weather are 3:2, this means:
- For every 3 favorable outcomes (good weather), there are 2 unfavorable outcomes (bad weather).

To find the **odds against** good weather, we simply reverse this ratio:
- The odds against good weather = 2:3.

So, the odds against good weather are **2:3**.

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### b) What is the **probability** of good weather tomorrow?

The odds in favor of good weather are given as 3:2. This tells us that out of a total of \( 3 + 2 = 5 \) possible outcomes, 3 of them are for good weather.

The probability of good weather is the ratio of favorable outcomes to the total outcomes:
\[
P(\text{good weather}) = \frac{3}{3 + 2} = \frac{3}{5}.
\]
So, the probability of good weather tomorrow is **0.6** or **60%**.

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Would you like any more details or have any questions? Here are some related questions for further exploration:

1. What are the odds in favor of bad weather tomorrow?
2. How do you convert odds into probability in general?
3. What are the odds against an event if the probability of it happening is \( \frac{1}{4} \)?
4. How do odds and probability differ in real-world applications?
5. If the probability of rain increases, how does that affect the odds?

**Tip:** To convert between odds and probability, use the formula \( P(A) = \frac{\text{odds in favor of A}}{1 + \text{odds in favor of A}} \).

1. Suppose the odds in favour of good weather tomorrow are 3:2.
a) What are the odds against good weather tomorrow?
b) What is the probability of good weather tomorrow?

Learn how to calculate the odds against good weather and the probability of good weather based on given odds in favor. This problem uses key concepts from probability and teaches how to convert odds to probability. Suitable for students in Grades 6-8.

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