Conditional Probability

May 19th, 2015
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If events A and B are independent, then the probability of B happening does not depend upon whether A has happened or not. Therefore P(B/A) = P(B/A') =P(B) A tree diagram can be drawn:

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Conditional ProbabilityRecap: 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 happening will depend upon whether A has happened or not.We therefore have to introduce conditional probabilities in the tree diagram (as shown below):The rule for combining probabilities for dependent events isP(A and B) = P(A) P(B | A)This is equivalent to sayingExample:Every morning I buy either The Times or The Mail. The probability that I buy The Times is and the probability that I buy The Mail is . If I buy The Times, the probability that I complete the crossword is , whereas if I buy The Mail the probability that I complete the crossword is .a) Find the probability that I complete the crossword on any particular day.b) If I have completed the crossword, find the probability that I bought The Mail.The tree diagram is:Notation: T = buy The TimesM = buy The MailC = complete crossworda) From the tree diagram,P(complete crossword

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