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`Conditional Probability


Recap: Independent events.

If events A and B are independent, then the probability of B happening does not depend upon whether A
has happened or not. Therefore







and

.


A tree diagram can be drawn:









Dependent events:

If A and B are dependent events, the probability of B…

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The rule for combining probabilities for dependent events is

P(A and B) = P(A) × P(B | A)

This is equivalent to saying






Example:
Every morning I buy either The Times or The Mail. The probability that I buy The Times is ¾ and the
probability that I buy The…

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Notation: T = buy The Times M = buy The Mail C = complete crossword

a) From the tree diagram,

P(complete crossword) = P(T and C) + P(M and C) =

b) The probability that I bought The Mail given that I completed the crossword is given by







Example 2:…

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Note: This example highlights the difficulty of detecting rare conditions or diseases.


Past Examination Question: (OCR)
Students have to pass a test before they are allowed to work in a laboratory. Students do not retake the
test once they have passed it. For a randomly chosen student, the probability of…

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