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(A) = 1/2 and A is acute, what is the value of A?

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What is the square root of 0.25?

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The base of a triangle is 10 cm and its height is 6 cm. What is its area?

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A sum of money triples itself in 12 years at simple interest. What is the rate of interest per annum?

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If the perimeter of a square is 40 cm, what is the area of the square?

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A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

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What is the sum of the first 50 positive integers?

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

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

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A train 120 meters long is moving at a speed of 54 km/h. How long will it take to pass a pole?

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