Topic Details (Notes format)

How to Identify Independent vs. Dependent Events

Subject: Mathematics

Book: Maths Mastery

Independent events do not affect each other’s outcome (e.g., rolling a die and flipping a coin), while dependent events do (e.g., drawing cards without replacement). Mathematically, events A and B are independent if P(A ∩ B) = P(A) × P(B). If they do not satisfy that, they are dependent. Understanding this difference is crucial in probability trees, combinatorial scenarios, or chain-of-event analyses. Correct classification ensures you multiply probabilities appropriately, whether you’re designing experiments or calculating risk in finance, health, or engineering contexts.

Practice Questions

If a:b = 7:9 and b:c = 5:6, what is a:c?

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A train 150 m long passes a pole in 15 seconds. What is its speed?

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If a square has a perimeter of 64 cm, what is its area?

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If the length of a rectangle is doubled and the width is halved, what is the change in area?

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What is the square root of 144?

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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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A number is increased by 20% and then decreased by 10%. What is the net change?

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If 8x = 512, what is the value of x?

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A number is increased by 20% and then decreased by 20%. What is the net change?

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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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