Calculating the chances of winning in fair games, like rolling a die or flipping a coin, is simple and can be a lot of fun! It’s all about knowing that every outcome has an equal chance and making sure the games are fair. Here’s how to break it down:

1. Understanding Outcomes:

When you flip a coin, there are two possible results: heads (H) or tails (T).

So, the total outcomes = 2.

When you roll a six-sided die, you can get six different results: 1, 2, 3, 4, 5, or 6.

So, the total outcomes = 6.

2. Determining Favorable Outcomes:

Next, let’s find the results that are good for what you want to know.

• Coin Example: If you want to know the chance of getting heads, there’s only 1 good result (H).
• Dice Example: If you want to know the chance of rolling a 4, there’s also just 1 good result (rolling a 4).

3. Calculating Probability:

Now we can figure out the probability using this formula:

Probability = Favorable Outcomes / Total Outcomes

• Coin Probability: For heads, it’s P(H) = 1/2 because there’s 1 good outcome out of 2 total outcomes.
• Dice Probability: For the number 4, it’s P(rolling a 4) = 1/6 because there’s 1 good outcome out of 6 total outcomes.

4. Experiments & Fairness:

You can test if these games are fair by doing them many times.

If you roll a die 60 times and each number shows up about 10 times, that means it’s fair!

In summary, by looking at the different outcomes and using the probability formula, you can find out the chances of different events in fair games. It’s like a mini science project that can lead to some fun discoveries!