When we talk about finding the chance of two events happening together in Year 7 Math, we are exploring how to figure out if two things can happen at the same time.

Understanding 'And' in Probability

When we say 'and' in probability, we want to know the likelihood of two events happening together. To calculate this chance, we use something called the multiplication rule. This rule tells us that if we want to find the probability of event A and event B happening at the same time, we multiply the chance of A by the chance of B.

The Formula

If we let $P(A)$ be the chance of event A and $P(B)$ be the chance of event B, the total chance of both events A and B happening together is:

$P(A \text{ and } B) = P(A) \times P(B)$

Example 1: Rolling Dice

Let’s understand this better with an example. Imagine you want to find the chance of rolling a 3 on a six-sided die and flipping a heads on a coin.

1. Calculate $P(A)$: The chance of rolling a 3 on a six-sided die is $P(A) = \frac{1}{6}$.

2. Calculate $P(B)$: The chance of flipping heads with a coin is $P(B) = \frac{1}{2}$.

Now, using the multiplication rule:

$P(\text{rolling a 3 and flipping heads}) = P(A) \times P(B) = \frac{1}{6} \times \frac{1}{2} = \frac{1}{12}$

Example 2: Drawing Cards

Let’s try another example with playing cards. What is the chance of drawing a heart and then an ace?

1. Calculate $P(A)$: The chance of drawing a heart from a standard deck is $P(A) = \frac{13}{52} = \frac{1}{4}$ because there are 13 hearts.

2. Calculate $P(B)$: If you want to find the chance of drawing an ace, there are 4 aces in total. So, $P(B) = \frac{4}{52} = \frac{1}{13}$.

Now we use the formula:

$P(\text{drawing a heart and then an ace}) = P(A) \times P(B) = \frac{1}{4} \times \frac{1}{13} = \frac{1}{52}$

Summary

To sum it all up, figuring out the probability of two events happening together with 'and' means you need to know the individual chances and use the multiplication rule. This method helps you see how likely different combinations of events are. Keep practicing with more examples, and soon this will become really easy for you!