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:b = 2:3 and b:c = 4:5, what is a:c?

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What is the square root of 0.25?

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What is the area of a sector of a circle with radius 14 cm and central angle 90°?

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If the sum of the squares of two consecutive positive integers is 365, what are the integers?

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The sides of a triangle are 7, 24, and 25. Is this a right triangle?

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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 x + y = 10 and xy = 21, what is the value of x³ + y³?

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What is the slope of a line passing through the points (2, 3) and (4, 7)?

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What is the sum of the first 50 positive integers?

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If x^2 - 6x + 9 = 0, what is the value of x?

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