Topic Details (Notes format)

How to Calculate Probability of Dependent Events

Subject: Mathematics

Book: Maths Mastery

Dependent events affect each other’s outcomes. The probability of both occurring is P(A) × P(B given A). For example, if you draw one card from a deck and do not replace it, drawing a second card changes the total card count, making the events dependent. If you want the probability of drawing two aces consecutively: P(first ace) = 4/52, then P(second ace given the first was ace) = 3/51, so the combined probability is (4/52) × (3/51). This concept applies in quality control, forecasting chain-of-event scenarios, and more. Understanding dependent probabilities clarifies how sequential conditions shape real-world outcomes.

Practice Questions

If the average of five consecutive odd numbers is 25, what is the largest number?

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

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

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What is the sum of all odd numbers from 1 to 99?

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If a:b = 3:4 and b:c = 5:6, what is a:c?

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What is the LCM of 15 and 20?

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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 slope of a line passing through the points (2, 3) and (4, 7)?

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

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