Topic Details (Notes format)

How to Use Probability Trees for Complex Probabilities

Subject: Mathematics

Book: Maths Mastery

Probability trees help map multi-stage or conditional events. Each branch holds a probability, and the product along a path yields the joint event probability. Summing relevant path probabilities solves “either/or” questions. For instance, flipping two coins can be diagrammed with branches for heads/tails at each step, calculating 1/4 probability for each HH, HT, TH, TT outcome. Probability trees excel in sequences: test performances, repeated draws without replacement, or multi-step game moves. This structured approach ensures no scenario is overlooked, promoting clarity in advanced probability analysis.

Practice Questions

A square is inscribed in a circle with a radius of 5 cm. What is the area of the square?

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If x^2 - 5x + 6 = 0, what are the roots?

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If the radius of a circle is 7 cm, what is its circumference?

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What is the HCF of 48 and 180?

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If the product of two numbers is 120 and their sum is 26, what are the numbers?

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If the sum of three consecutive integers is 96, what are the integers?

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The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

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If 5x - 2 = 13, what is the value of x?

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If sin(θ) = 3/5 and θ is an acute angle, what is tan(θ)?

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How many ways can 4 people sit in a row?

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