Solve this:
Manpreet and her friends meet every Thursday night to play a different sport.When they play basketball, she has a 75% chance of being on the winning team.Considering their game next week, if there is a 40% chance they will playbasketball then what are the odds in favour of Manpreet being on the winningteam of a basketball game?
(4 marks)

### Problem Breakdown:

- Manpreet and her friends meet every Thursday night to play a sport.
- There is a **40% chance** that they will play basketball next week.
- If they play basketball, Manpreet has a **75% chance** of being on the winning team.
- We need to find the **odds in favor** of Manpreet being on the winning team in a basketball game next week.

### Step 1: Probability that Manpreet is on the winning team.
The probability \( P(\text{Winning}) \) of Manpreet being on the winning team next week can be calculated by multiplying:
1. The probability that they play basketball.
2. The probability that Manpreet is on the winning team if they play basketball.

This gives us:
\[
P(\text{Winning}) = 0.40 \times 0.75 = 0.30
\]
So, the probability that Manpreet will be on the winning team next week is \( 0.30 \) or \( 30\% \).

### Step 2: Odds in Favor of Winning.
The odds in favor of an event are defined as:
\[
\text{Odds in favor} = \frac{\text{Probability of success}}{\text{Probability of failure}}
\]
Here, the probability of success (Manpreet being on the winning team) is \( 0.30 \), and the probability of failure (not being on the winning team) is \( 1 - 0.30 = 0.70 \).

Thus, the odds in favor are:
\[
\text{Odds in favor} = \frac{0.30}{0.70} = \frac{3}{7}
\]

### Final Answer:
The odds in favor of Manpreet being on the winning team are **3:7**.

Would you like any further clarification or details?

Here are five related questions you might consider:
1. How would the odds change if the probability of playing basketball increased?
2. What would be the odds against Manpreet winning next week?
3. How do odds differ from probability in this context?
4. If Manpreet's chance of winning was 80%, what would the new odds be?
5. How would you express the odds in favor of Manpreet losing?

**Tip:** When converting probability to odds, remember that odds express the ratio of success to failure, not just the success rate itself!

Manpreet and her friends meet every Thursday night to play a different sport. When they play basketball, she has a 75% chance of being on the winning team. Considering their game next week, if there is a 40% chance they will play basketball, what are the odds in favour of Manpreet being on the winning team of a basketball game?

Learn how to calculate the odds of Manpreet being on the winning team in a basketball game. This problem involves understanding probability and calculating odds, making it suitable for students in Grades 6-8. Includes step-by-step solution with key formulas.

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