Probability & Statistics

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Probability of Multiple Events

We can combine probabilities to find the probability that multiple events will all happen

When we combine probabilities, we can find the probability of two events happening together.

To find the combined probability of two events happening, we need to multiply the probabilities together. This is called the and rule of probability.

For example, the probability of it raining tomorrow is $\dfrac{1}{5}$ . The probability of your car not starting is $\dfrac{2}{10}$ . To find the probability of both happening, we multiply these together:

$\frac{1}{5}\times\frac{2}{10}=\frac{2}{50}$

Let's try an example. You roll a 4-sided spinner and a standard die. What is the probability of landing on a 2 on both?

Find the probability of landing on a 2 on the die

The probability is $\dfrac{1}{6}$

Landing on a 2 represents 1 of a possible 6 outcomes on the die.

What is the probability of a 2 on the spinner?

The probability is $\dfrac{1}{4}$

Landing on a 2 on the spinner represents 1 of a possible 4 total outcomes.

Combine these probabilities

To find the combined probability, we need to multiply them together.

What is the combined probability of both events?

What is the probability of landing on a 1 when rolling a fair 6-sided die and landing on a tail when flipping a fair £1 coin?