Statistics & Probability

AdvancedMaths revision

Probability: Counting & Bayes

Handle conditional probability, counting, repeated trials and dependent events in multi-stage problems.

Open calculator

Focus points

✓Use tree and Venn structures.

✓Count outcomes efficiently.

✓Distinguish dependent and independent events.

orin

Orin

The Wise Owl

Guides study flow, revision planning, and calmer focus sessions.

Practice set

Question lineup

Try each question first, reveal a hint when you need one, then check the worked answer. Mark them done as you go — finish the set to claim your chips.

8 revision questions

Question 1FluencyCore

Original practice · Free Online Revision

Skill · without replacement

A box has 5 red,4 blue,3 green counters. Two are drawn without replacement. Find P(both blue).

Question 2FluencyCore

Original practice · Free Online Revision

Skill · tree probability

For the same box, find P(one red and one green in any order).

Question 3FluencyCore

Original practice · Free Online Revision

Skill · Venn probability

If P(A)=0.6,P(B)=0.5,P(A∩B)=0.3, find P(A∪B).

Question 4FluencyCore

Original practice · Free Online Revision

Skill · binomial counting

A fair coin is tossed 5 times. Find P(exactly 3 heads).

Question 5FluencyCore

Original practice · Free Online Revision

Skill · counting principle

A 4-digit PIN uses digits 0–9 with repetition allowed. How many PINs are possible?

Question 6FluencyCore

Original practice · Free Online Revision

Skill · permutations

How many 4-letter arrangements can be made from A,B,C,D,E without repetition?

Question 7FluencyCore

Original practice · Free Online Revision

Skill · combinations

A class has 8 students; choose a committee of 3. How many committees?

Question 8ChallengeStretch

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Skill · Bayes theorem

A factory has machines M1 and M2 producing 70% and 30% of items. Defect rates are 2% and 5%. Given an item is defective, find P(it came from M2).