Topic Details (Notes format)

How to Solve Conditional Probability Problems

Subject: Mathematics

Book: Maths Mastery

Conditional probability P(A|B) measures the likelihood of A given B has occurred, computed as P(A ∩ B) ÷ P(B). For example, if the probability of it raining and your friend carrying an umbrella is 0.30, and the probability of your friend carrying an umbrella is 0.50, then P(Rain|Umbrella) = 0.30 ÷ 0.50 = 0.60. Conditional probability arises in medical testing (positive test given the condition), machine learning (predictive models), and daily logic (likelihood of an outcome given partial info). Mastering it refines your reasoning and real-life decision-making based on evolving evidence.

Practice Questions

If sin(θ) = 0.6 and θ is acute, what is cos(θ)?

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A square is inscribed in a circle with a radius of 5 cm. What is the area of the square?

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If 2x - 3 = 7, what is the value of x?

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

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

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The area of an equilateral triangle with side length 6 cm is:

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If the cost price of an item is Rs. 400 and the selling price is Rs. 500, what is the profit percentage?

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What is the greatest common divisor (GCD) of 36 and 48?

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