What is a sample space?

The set of all possible outcomes.

What does mutually exclusive mean?

The events cannot happen together: P(A\cap B)=0.

Addition rule for any two events?

P(A\cup B)=P(A)+P(B)-P(A\cap B)

Why subtract P(A\cap B) in the addition rule?

The overlap is counted twice when P(A) and P(B) are added.

How many equally likely outcomes for two fair dice?

36 for two six-sided dice (16 for two four-sided dice).

Elementary probability and sample spacesEdexcel International A Level Maths: Flashcards

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Probability of an event with equally likely outcomes?

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Probability of an event with equally likely outcomes?: $P(A)=\frac{\text{outcomes in }A}{\text{total outcomes}}$
What is a sample space?: The set of all possible outcomes.
Formula for the complement?: $P(A')=1-P(A)$
What does $A\cup B$ mean?: $A$ or $B$ or both.
What does $A\cap B$ mean?: Both $A$ and $B$ .
What does mutually exclusive mean?: The events cannot happen together: $P(A\cap B)=0$ .
Addition rule for any two events?: $P(A\cup B)=P(A)+P(B)-P(A\cap B)$
Addition rule for mutually exclusive events?: $P(A\cup B)=P(A)+P(B)$
Why subtract $P(A\cap B)$ in the addition rule?: The overlap is counted twice when $P(A)$ and $P(B)$ are added.
How do you find $P(\text{at least one})$ quickly?: $1-P(\text{none})$
Formula for $P(A\cap B')$ ?: $P(A)-P(A\cap B)$
Formula for $P(A'\cap B')$ ?: $1-P(A\cup B)$
How many equally likely outcomes for two fair dice?: 36 for two six-sided dice (16 for two four-sided dice).

Exam questions on Elementary probability and sample spaces

A fair six-sided die is rolled once. Event $A$ is 'the score is even' and event $B$ is 'the score is greater than 3'.
Explain why $A$ and $B$ are not mutually exclusive.2 marks
Two fair four-sided dice, each numbered 1, 2, 3 and 4, are rolled and the two scores are added.
Find the probability that the total score is a prime number.2 marks
In a class of 40 students, 22 study French ( $F$ ), 18 study Spanish ( $S$ ) and 9 study both. One student is chosen at random.
Find the probability that the student studies French or Spanish (or both).3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).