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 = 10 and ab = 21, what is the value of (a-b)^2?

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

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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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What is the 7th term of the arithmetic progression 3, 6, 9, 12,...?

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A rectangle has a length of 10 cm and a width of 5 cm. What is the diagonal of the rectangle?

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

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If the sum of the angles of a polygon is 1080°, how many sides does the polygon have?

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What is the remainder when 5^100 is divided by 3?

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What is the area of a circle with a diameter of 14 cm?

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If 2x = 16, what is the value of x?

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