When you are finding the probability of a single event, it is fairly straightforward to find the probability of something happening.

But what about when there are multiple events happening. When I introduce this in school, I start by asking how many things could happen if I rolled two dice and I always get the (incorrect) answer 12.

To solve problems like this, we need to consider all the outcomes and list them systematically.

If I roll a 1 on the first die, there are 6 things that could happen on the second die.

If I roll a 2 on the first die, there are 6 things that could happen on the second die.

etc etc

**Is there a quick way?**

Yep, there certainly is. If you have 6 outcomes on the first thing and 6 on the second thing, there will be 6 x 6 = 36 outcomes

**Multiply the ****amount**** of outcomes for each event to get the total number of event.**

**Example 1: I throw a coin and roll a dice. list all the possible outcomes.**

We need to do this logically.

If I throw a head on the coin, I could get the numbers 1 - 6 on the dice.

**H1 H2 H3 H4 H5 H6**

If I throw a tail on the coin, I could get the number 1 - 6 on the dice

**T1 T2 T3 T4 T5 T6**

As a double check, I have 2 outcomes on the coin and 6 on the dice. This means I should have 2 x 6 = 12 outcomes. (And I do!)

**Example 2: I throw a coin and roll a dice. what is the probability I get a head and an even number?**

Our first step here is to list all the outcomes.

**H1 H2 H3 H4 H5 H6 **

**T1 T2 T3 T4 T5 T6**

We can now identify which ones satisfy our condition (head and even)

**H1 ****H2**** H3**** H4**** H5 ****H6 **

**T1 T2 T3 T4 T5 T6**

We can see there are 3 outcomes that satsify the condition and 12 in total.

This gives a probability of 3/12 which simplifies to 1/4