Probability | Perplex

Probability

Video Reviews

Watch comprehensive video reviews for Probability, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.

Not your average video:

Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

Not your average video:

Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

TerminologyCombined EventsBayes Theorem

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Venn Diagrams

SL 4.6

A Venn diagram is a visual tool used to illustrate relationships between sets or events. Each event is represented by a circle, and overlaps between circles represent shared outcomes. This helps you clearly see intersections (outcomes common to events), unions (all outcomes in any event), and mutually exclusive events (no overlap).

Example

Using the following Venn diagram, find

n(U)
P(A∩B)
P(A∩C)
P(A′∪C)

Powered by Desmos

In the above Venn diagram, we start by noticing

n(U)=5+2+11+3+8=29

We also notice that A and B do not overlap - so they are mutually independent:

P(A∩B)=0

We see that the region shared by A and C has a 2, so

P(A∩C)=292

Finally

P(A′∩C)=P(C)−P(C∩A)=2915−2=2913

Venn Diagrams

SL 4.6

A Venn diagram is a visual tool used to illustrate relationships between sets or events. Each event is represented by a circle, and overlaps between circles represent shared outcomes. This helps you clearly see intersections (outcomes common to events), unions (all outcomes in any event), and mutually exclusive events (no overlap).

Example

Using the following Venn diagram, find

n(U)
P(A∩B)
P(A∩C)
P(A′∪C)

Powered by Desmos

In the above Venn diagram, we start by noticing

n(U)=5+2+11+3+8=29

We also notice that A and B do not overlap - so they are mutually independent:

P(A∩B)=0

We see that the region shared by A and C has a 2, so

P(A∩C)=292

Finally

P(A′∩C)=P(C)−P(C∩A)=2915−2=2913