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

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If the perimeter of a square is 36 cm, what is the length of its diagonal?

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

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

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

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If 2a + b = 10 and a - b = 4, what is the value of a?

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

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If a:b = 5:7 and b:c = 6:11, what is a:c?

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What is the square root of 144?

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What is the area of an equilateral triangle with side length 10 cm?

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