 # Use Two Event Probability

In this worksheet, students practise listing all the outcomes of multiple events and using them to find probabilities. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Probability

Curriculum subtopic:   Probability, Basic Probability and Experiments

Difficulty level:   ### QUESTION 1 of 10

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

A spinner has 3 outcomes and a coin has two.

If I spin the spinner and throw the dice at the same time, how many events could happen?

6

5

I have 2 spinners.

Spinner 1 has a outcomes

Spinner 2 has b outcomes.

How many outcomes will I have if i spin the spinners together?

If I flip two coins together. What are the different outcomes?

 - Outcome 1 Outcome 2 Outcome 3 Outcome 4

I throw two coins together.

What is the probability that at least one of them will be a tail?

I throw two coins together.

What is the probability I will get the same on both coins?

A spinner has three colours (Red, Yellow and Blue).

How many times would I have to spin it to have more than 100 different outcomes?

A coin and a dice are thrown together. By listing all the outcomes, find the probability I get a head and a 6.

A coin and a dice are thrown together. By listing all the outcomes, find the probability I get Tails and an even.

A coin and a dice are thrown together. By listing all the outcomes, find the probability I get Tails and a number less than 7

Match the situations with the number of outcomes.

## Column B

A coin and a dice
12
two dice
24
4 coins
36
two coins and a dice
16
• Question 1

A spinner has 3 outcomes and a coin has two.

If I spin the spinner and throw the dice at the same time, how many events could happen?

6
EDDIE SAYS
The common mistake with this question is to add the outcomes together. Think of it as 3 lots of 2 . The words lots of in Maths means multiply.
• Question 2

I have 2 spinners.

Spinner 1 has a outcomes

Spinner 2 has b outcomes.

How many outcomes will I have if i spin the spinners together?

ab
a x b
ax b
a xb
EDDIE SAYS
This does look a bot more complicated than the last question but it's just exactly the same. All we have to do is multiply the individual outcomes, it's just a bit of simple algebra. a x b = ab outcomes
• Question 3

If I flip two coins together. What are the different outcomes?

 - Outcome 1 Outcome 2 Outcome 3 Outcome 4
EDDIE SAYS
The first thing we need to do with a question like this is to think logically. If I get heads on coin 1, I could get heads or tails on coin 2 (HH HT) If I get tails on coin 1, I could get heads or tails on coin 2 (TH TT)
• Question 4

I throw two coins together.

What is the probability that at least one of them will be a tail?

3/4
EDDIE SAYS
If we look at the outcomes from the previous question HH HT TH TT We can see that three of them have at least one tail out of the 4.
• Question 5

I throw two coins together.

What is the probability I will get the same on both coins?

1/2
EDDIE SAYS
If we look at the outcomes from the previous question HH HT TH TT We can see that two of four of them have the same outcomes (HH and TT)
• Question 6

A spinner has three colours (Red, Yellow and Blue).

How many times would I have to spin it to have more than 100 different outcomes?

5
EDDIE SAYS
Lets think about this. If I spin it once, I have 3 outcomes If I spin it twice, I would have 3 x3 = 9 outcomes If I spin it three times, I would have 3 x 3 x 3 = 27 outcomes If I spin it four times....
• Question 7

A coin and a dice are thrown together. By listing all the outcomes, find the probability I get a head and a 6.

1/12
EDDIE SAYS
If we start by listing all the outcomes... H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6 We can see that there is only one way of getting a head and a six out of the 12 outcomes
• Question 8

A coin and a dice are thrown together. By listing all the outcomes, find the probability I get Tails and an even.

1/4
EDDIE SAYS
If we start by listing all the outcomes... H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6 We can see that there are three ways of getting tails and an even out of the 12 outcomes
• Question 9

A coin and a dice are thrown together. By listing all the outcomes, find the probability I get Tails and a number less than 7

1/2
EDDIE SAYS
If we start by listing all the outcomes... H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6 We can see that there are six ways of getting tails and a number less than 7 out of the 12 outcomes The other way we could look at this is that we must get a number less than 7 on the dice, so we can ignore the probability and just use the probability of getting tails on the dice.
• Question 10

Match the situations with the number of outcomes.

## Column B

A coin and a dice
12
two dice
36
4 coins
16
two coins and a dice
24
EDDIE SAYS
Remember right back to the start, if you want the total outcomes, you have to multiply the outcomes for each one to find the total. So if I had a spinner with 3 options and a dice. I would have 3 x 6 = 18 options.
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