Calculating the chance of simple events is an important topic in Year 7 Math. It helps students see how likely something is to happen. This guide explains how to find probabilities easily, using examples like rolling a die and flipping a coin.

Key Ideas About Probability

First, let's look at some important terms:

• Experiment: An action that leads to a result, like rolling a die.
• Outcome: The result from one trial of an experiment, like rolling a 3.
• Sample Space (S): All the possible outcomes of an experiment. For a die, $S = \{1, 2, 3, 4, 5, 6\}$.
• Event: A specific outcome we care about. For example, rolling an even number.

Steps to Calculate Probability

1. Identify the Experiment and Outcomes:

   • Figure out what the experiment is. For rolling a die, the outcomes are numbers 1 to 6.
   • Write the sample space. For a die, it looks like this:
   $$S = \{1, 2, 3, 4, 5, 6\}$$

2. Count the Total Number of Outcomes:

   • Count how many outcomes there are. For a die, there are 6 possible outcomes.

3. Define the Event:

   • Decide what event you want to find the chance of. For example, let's look at rolling a number greater than 4. The outcomes for this event are $\{5, 6\}$.

4. Count the Favorable Outcomes:

   • See how many outcomes fit your event. Here, there are 2 outcomes that match (5 and 6).

5. Use the Probability Formula:

   • To find the probability of an event, use this formula:
   $$P(E) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}}$$
   • For rolling a number greater than 4:
   $$P(\text{rolling > 4}) = \frac{2}{6} = \frac{1}{3}$$

6. Simplify the Probability:

   • Try to make the fraction simpler. Here, $\frac{2}{6}$ simplifies to $\frac{1}{3}$.

7. Convert to Decimal or Percentage (if needed):

   • Sometimes it's easier to show the probability as a decimal or percentage:
   • As a decimal: $P(\text{rolling > 4}) \approx 0.33$
   • As a percentage: $P(\text{rolling > 4}) = 33.33\%$

Example: Flipping a Coin

Let's look at the chance of simple events using a coin flip.

1. Identify the Experiment and Outcomes:

   • The experiment is flipping a coin, which has two outcomes: heads (H) and tails (T).
   • The sample space is:
   $$S = \{H, T\}$$

2. Count the Total Number of Outcomes:

   • There are 2 outcomes when you flip a coin.

3. Define and Count the Favorable Outcomes:

   • If we're looking for the chance of flipping heads, there's 1 favorable outcome (H).

4. Use the Probability Formula:

   • Apply the formula:
   $$P(H) = \frac{1}{2}$$

5. Simplify and Convert if Needed:

   • This is already simple. As a decimal, $P(H) = 0.5$, and as a percentage, $P(H) = 50\%$.

Conclusion

By following these steps, Year 7 students can easily calculate the chances for simple events. Understanding these ideas is important for a strong foundation in probability and statistics.