2026 views

### How can I know whether to multiply or add probabilities?

We can only add probabilities when the events are alternatives. For example, let's say we want to calculate the probability that we achieve an A or a B or a C in a given exam. We cannot achieve an A and B for the same exam, so these events are indeed alternatives.

So let's say there's a 1/10 chance of getting an A, a 3/10 chance of getting a B and 4/10 chance of getting a C. The chance that we get either an A, B or C would be the sum of the individual probabilities: (1/10 + 3/10 + 4/10), so 8/10.

Think about the problem numerically. We know that all probabilities lie in the range from 0 to 1. Addition of such numbers will lead to an increased probability value. Multiplication of such numbers will lead to a decreased probability value. In this case, we'd expect the probability of attaining A or B or C to be greater than the probability of simply attaining an A. And yes, we have an 8/10 chance of attaining an A,B or C and only a 1/10 chance of attaining an A - this is what we'd expect.

We multiply probabilites when we want events to occur simultaneously, or consecutively. Let's say we're going to sit the same exam twice. We want to find the probability of attaining a C first time and an A on the re-sit. Before we dive in let's think about the expected probability value: getting a C AND THEN an A is a very unique scenario, and as such we'd expect quite a low probability in relation to the probabilities of individual events. This hints to us that multiplication could be the correct method.

So in this case, yes, we can say that the probability of getting a C and then an A is (4/10 * 1/10), so 1/25.

2 years ago

Answered by Nathan, a GCSE Maths tutor with MyTutor

## Still stuck? Get one-to-one help from a personally interviewed subject specialist

#### 781 SUBJECT SPECIALISTS

£18 /hr

Degree: Philosophy, Politics and Economics (Bachelors) - Oxford, Worcester College University

Subjects offered:Maths, Spanish+ 5 more

Maths
Spanish
History
Economics
.TSA. Oxford.
-Personal Statements-
-Oxbridge Preparation-

“I am an aspiring teacher, with a clear and analytic approach to tutoring that comes from an extensive and varied educational background.”

£24 /hr

Degree: Mathematics MMath (Masters) - Manchester University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Hello there, I'm Mark and I study Mathematics at the University of Manchester! Let me help you achieve your best!”

£18 /hr

Degree: MSc Financial Analysis and Fund Management (Masters) - Exeter University

Subjects offered:Maths, Economics

Maths
Economics

Currently unavailable: no new students

Degree: Computer Science (Bachelors) - Manchester University

Subjects offered:Maths, Physics

Maths
Physics

“Friendly Computer Science undergraduate at the University of Manchester. I'm here to help you with Maths and Physics at GCSE, A level or IB”

MyTutor guarantee

### You may also like...

#### Other GCSE Maths questions

How do I complete the square of an equation?

Kieran, Jermaine and Chris play football. Kieran has scored 8 more goals than Chris. Jermaine has scored 5 more goals than Kieran. Altogether they have scored 72 goals. How many goals did Jermaine score?

Solve the simultaneous equations: 4x+3y=5 and x-y=3, to find the values of x and y.

What is Pythagoras' Theorem and how do you use it?

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this.