General addition law?

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

Independence in conditional form?

P(B\mid A)=P(B) and P(A\mid B)=P(A)

How do you test whether A and B are independent?

Compare P(A\cap B) with P(A)P(B); they must be equal.

Can two events with non-zero probabilities be both mutually exclusive and independent?

No: P(A\cap B)=0 but P(A)P(B)0.

In a tree diagram, what do you do along and between branches?

Multiply along a path; add between paths.

For a continuous variable, what is P(X=a)?

0, because a single value has no area.

What do the probabilities of a discrete distribution add up to?

1, as the values are mutually exclusive and exhaustive.

Mutually exclusive and independent eventsEdexcel A-Level Maths: Flashcards

Card 1 of 130 of 13 known

Question

What does mutually exclusive mean?

Tap or press Space to reveal

Tap card or press Space to flip

See all 13 cards

What does mutually exclusive mean?: The events cannot both occur, so $P(A\cap B)=0$ .
Addition law for mutually exclusive events?: $P(A\cup B)=P(A)+P(B)$
General addition law?: $P(A\cup B)=P(A)+P(B)-P(A\cap B)$
Condition for independent events?: $P(A\cap B)=P(A)P(B)$
Independence in conditional form?: $P(B\mid A)=P(B)$ and $P(A\mid B)=P(A)$
How do you test whether $A$ and $B$ are independent?: Compare $P(A\cap B)$ with $P(A)P(B)$ ; they must be equal.
Can two events with non-zero probabilities be both mutually exclusive and independent?: No: $P(A\cap B)=0$ but $P(A)P(B)>0$ .
$A$ and $B$ independent, $P(A)=0.4$ , $P(B)=0.5$ : $P(A\cup B)$ ?: $0.4+0.5-0.2=0.7$
If $A$ and $B$ are independent, what about $A$ and $B'$ ?: They are also independent.
In a tree diagram, what do you do along and between branches?: Multiply along a path; add between paths.
What represents probability for a continuous random variable?: Area under the curve.
For a continuous variable, what is $P(X=a)$ ?: $0$ , because a single value has no area.
What do the probabilities of a discrete distribution add up to?: $1$ , as the values are mutually exclusive and exhaustive.

Exam questions on Mutually exclusive and independent events

Events $A$ and $B$ are mutually exclusive, with $P(A)=0.3$ and $P(B)=0.4$ .
Show that $A$ and $B$ are not independent.2 marks
Events $C$ and $D$ are independent, with $P(C)=0.6$ and $P(D)=0.25$ .
Find $P(C\mid D')$ .2 marks
Events $A$ and $B$ are independent, with $P(A)=0.2$ and $P(A\cup B)=0.6$ . Event $E$ is mutually exclusive with $A$ and also mutually exclusive with $B$ , and $P(E)=0.3$ .
Find $P(B)$ .3 marks

See the full worksheet

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).