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

If a cone has a radius of 5 cm and a height of 12 cm, what is its slant height?

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The sides of a triangle are 5 cm, 12 cm, and 13 cm. What type of triangle is it?

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If the perimeter of a square is 40 cm, what is the area of the square?

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What is the sum of the first 10 positive even numbers?

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A sum triples in 20 years at simple interest. What is the rate of interest per annum?

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If x² - 9x + 18 = 0, what are the roots of the equation?

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If x = 2 and y = 3, what is the value of (x^2 + y^2)?

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What is the length of the diagonal of a square with a side length of 7 cm?

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If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

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If x^2 + 4x + 4 = 0, what is the value of x?

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