When you're learning about probability in Year 9, it’s easy to make a few common mistakes. I’ve noticed these issues in discussions and homework, so I want to share some tips to help you avoid them.

Mistake 1: Mixing Up Independent and Dependent Events

A big mistake students make is not knowing the difference between independent and dependent events.

• Independent Events: These are events that don’t affect each other. For example, flipping a coin and rolling a die. The result of one doesn’t change the other. To figure out the probability of both happening, you can use this formula: $P(A \text{ and } B) = P(A) \times P(B)$

• Dependent Events: These events do affect each other. A good example is drawing cards from a deck without putting them back. The probability changes every time you draw. If you want to find the chance of drawing two aces in a row, it looks like this: $P(A \text{ and } B) = P(A) \times P(B|A)$ Here, $P(B|A)$ means the chance of getting B after getting A.

Mistake 2: Getting the Addition Rule Wrong

Another common mistake happens with the Addition Rule. Students sometimes forget to check if the events can happen together.

• Mutually Exclusive Events: These events can’t happen at the same time. For example, if you roll a die, you can’t roll a 2 and a 5 at the same time. For two mutually exclusive events, the formula is: $P(A \text{ or } B) = P(A) + P(B)$

• Non-Mutually Exclusive Events: If the events can happen at the same time, you need to subtract the overlap. For instance, to find the chance of drawing a heart or a queen from a deck of cards, you use: $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$

Mistake 3: Using Percentages Wrongly

Sometimes, students use percentages without changing them to probabilities. Remember, probabilities should be a number between 0 and 1, or as a fraction.

• If someone says there’s a 25% chance of something happening, that’s like saying the probability is $0.25$ or $\frac{1}{4}$. Make sure to change percentages correctly before using the addition or multiplication rules.

Mistake 4: Forgetting Total Probabilities

Lastly, always remember that the total probability of all possible outcomes should equal 1. If your probabilities add up to more than 1, you’ve probably made a mistake. This is a good sign to double-check your work and make sure you’ve counted all outcomes.

Conclusion

By understanding these common mistakes, you can make your work with probability easier. Remember to check if events are independent or dependent, know the difference between mutually exclusive and non-mutually exclusive events, convert percentages correctly, and keep track of your totals. The more you practice these concepts, the easier they will become. Good luck!