What does P(A\mid B) mean in words?

Probability of A given that B has occurred.

Is P(A\mid B)=P(B\mid A) in general?

No; the denominators differ (P(B) and P(A)).

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

What do second-stage tree branches show?

Conditional probabilities, given the first-stage outcome.

Conditional probability and tree and Venn diagramsEdexcel A-Level Maths: Flashcards

Card 1 of 130 of 13 known

Question

Formula for $P(A\mid B)$?

Tap or press Space to reveal

Tap card or press Space to flip

See all 13 cards

Formula for $P(A\mid B)$ ?: $\frac{P(A\cap B)}{P(B)}$
Multiplication law?: $P(A\cap B)=P(A\mid B)P(B)$
What does $P(A\mid B)$ mean in words?: Probability of $A$ given that $B$ has occurred.
Is $P(A\mid B)=P(B\mid A)$ in general?: No; the denominators differ ( $P(B)$ and $P(A)$ ).
Complement rule?: $P(A')=1-P(A)$
Addition law?: $P(A\cup B)=P(A)+P(B)-P(A\cap B)$
How do you find $P(B\cap A')$ from $P(B)$ and $P(A\cap B)$ ?: $P(B)-P(A\cap B)$
Conditional form of independence?: $P(A\mid B)=P(A)$
In a tree diagram, what do you do along a path and between paths?: Multiply along; add between.
In a tree diagram, what must branches from one point add to?: $1$
What do second-stage tree branches show?: Conditional probabilities, given the first-stage outcome.
On a Venn diagram, what is filled in first?: The intersection $A\cap B$ .
Counts: 20 of 50 do $A$ , 8 do $A$ and $B$ , 30 do $B$ . $P(A\mid B)$ ?: $\frac{8}{30}$

Exam questions on Conditional probability and tree and Venn diagrams

Of 50 sixth-form students, 28 study Mathematics, 20 study Physics and 8 study both subjects. One of the 50 students is chosen at random.
Given that the student studies exactly one of the two subjects, find the probability that it is Mathematics.2 marks
On any day, the probability that it rains is $0.3$ . When it rains, the probability that a certain bus is late is $0.4$ . When it does not rain, the probability that the bus is late is $0.1$ .
Given that the bus is not late, find the probability that it did not rain.2 marks
Events $A$ and $B$ are such that $P(A)=0.6$ , $P(B)=0.5$ and $P(A\mid B)=0.4$ .
Find $P(A\cup B)$ .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).