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

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

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A car travels 240 km in 4 hours. What is its average speed?

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What is the cube root of 729?

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If x + y = 10 and xy = 21, what is the value of x³ + y³?

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

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What is the sum of all even numbers between 1 and 100?

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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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The LCM of 12 and 15 is:

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If x^2 - 5x + 6 = 0, what are the roots?

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