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AQ0023 Note 10 Probability 2.pdf - A conditional...

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05/12/2015 1 ° A conditional probability is the probability of an event occurring, given that another event has already occurred. ° The conditional probability of event B occurring given that event A has occurred, is denoted by P(B|A) and is read as “probability of B, given A”. 2
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05/12/2015 2 3 ° Table below shows the results of a study in which researchers examined a child’s IQ and the presence of a specific gene in the child. Find the probability that a child, ° does not have the gene. ° has a high IQ given that the child has the gene. ° does not have the gene given that the child has a normal IQ. A person owns a collection of 30 CDs, of which 5 are country music. a) 2 CDs are selected at random and with replacement. Find the probability that the second CD is country music given that the first CD is country music. b) This time the selection made is without replacement. Find the probability that the second CD is country music given that the first CD is country music. 4
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05/12/2015 3 ° In some experiments, one event does not affect the probability of another. ° Example: Roll a die and toss a coin. The outcome of the roll of the die does not affect the probability of the coin landing on heads these two events are independent. ° We can use conditional probabilities to determine whether events are independent. ° Two events are independent if the occurrence of one of the events does not affect the probability of the occurrence of the other event. ° Events that are not independent are dependent. 5 6 ° Classify whether the events are independent or dependent. ° Tossing a coin and getting a head (A), and then rolling a die and obtaining a 6 (B) ° Selecting a king from a standard deck (A), not replacing it, and then selecting a queen from the deck (B) ° Driving over 135 kilometer per hour (A), and then getting in a car accident (B) ° Smoking a pack of cigarettes per day (A) and developing emphysema, a chronic lung disease (B) ° Exercising frequently (A) and having a 4.0 grade point average (B)
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05/12/2015 4 ° Two events A and B are independent if ° To determine whether A and B are independent ° 1st: Calculate the probability of event B, P(B) ° 2nd: Calculate the probability of B given A, P(B|A) ° 3rd: If the values are equal [P(B) = P(B|A)], the events are independent.
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