# Conditional Probability

Conditional Probability, probability, tree diagram

HideShow resource information
Word Document 87 Kb

## Pages in this set

### Page 1

`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…

### Page 2

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

### Page 3

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:…

### Page 4

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…