Conditional Probability Conditional Probability PA B means the
Conditional Probability
Conditional Probability P(A B) means “the probability that event A occurs given that B has occurred”.
Conditional Probability Example Low Medium High Male 12 33 7 Female 23 21 4 Total Find P(F L) Total 100
Conditional Probability Solution: Male Female Low 12 23 35 Medium 33 21 High 7 4 Total 100 Find P(F L) = The probability of selecting a female given the car is low rated.
Example Conditional Probability A sample of 100 adults were asked how they travelled to work. The results are shown in the table. Walk Bus Bike Car Men 10 12 6 26 Women 7 18 4 17 Total 100 One person is picked at random. M is the event “the person is a man” C is the event “the person travels by car” Find P(M C) P(C M/)
Conditional Probability Solution: Walk Bus Bike Car Men 10 12 6 26 54 Women 7 18 4 17 46 43 100 Total Find (i) P(M C) = P(C M/) = (ii) P(M C) (iii) P(M/ and C) (iv) P(C M/)
Conditional Probability • If you don’t have a table, you can use this formula
Conditional Probability Researchers asked people who exercise regularly whether they jog or walk. Fifty-eight percent of the respondents were male. Twenty percent of all respondents were males who said they jog. Find the probability that a respondent jogs given that they are a male. P( male ) = 58% P( male and jogs ) = 20% Let A = male. Let B = jogs. Write: P( A | B ) = = 0. 2 0. 58 P( A and B ) P( A ) Substitute 0. 2 for P(A and B) and 0. 58 for P(A). 0. 344 Simplify. The probability that a male respondent jogs is about 34%.
Conditional Probability Independent Events If the probability of the occurrence of event A is the same regardless of whether or not an outcome B occurs, then the outcomes A and B are said to be independent of one another. Symbolically, if then A and B are independent events.
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