A card is drawn from a standard deck. Find the probability of drawing an ace or a king. Using the Complement Rule to Compute Probabilities We have discussed how to calculate the probability that an event will happen. Sometimes, we are Interested in finding the probability that an event will not happen. The complement of an event E, denoted E’,is the set of outcomes in the sample space that are not in E. For example, suppose we are interested in the probability that a horse will lose a race. If event W is the horse winning the race, then the complement of event W is the horse losing the race. To find the probability that the horse loses the race, we need to use the fact that the sum of all probabilities in a probability model must be 1. P ( E ’ ) = 1 − P ( E ) The probability of the horse winning added to the probability of the horse losing must be equal to 1. Therefore, if the probability of the horse winning the race is 1 9 ,the probability of the horse losing the race is simply. 1 − 1 9 = 8 9
A card is drawn from a standard deck. Find the probability of drawing an ace or a king. Using the Complement Rule to Compute Probabilities We have discussed how to calculate the probability that an event will happen. Sometimes, we are Interested in finding the probability that an event will not happen. The complement of an event E, denoted E’,is the set of outcomes in the sample space that are not in E. For example, suppose we are interested in the probability that a horse will lose a race. If event W is the horse winning the race, then the complement of event W is the horse losing the race. To find the probability that the horse loses the race, we need to use the fact that the sum of all probabilities in a probability model must be 1. P ( E ’ ) = 1 − P ( E ) The probability of the horse winning added to the probability of the horse losing must be equal to 1. Therefore, if the probability of the horse winning the race is 1 9 ,the probability of the horse losing the race is simply. 1 − 1 9 = 8 9
A card is drawn from a standard deck. Find the probability of drawing an ace or a king. Using the Complement Rule to Compute Probabilities We have discussed how to calculate the probability that an event will happen. Sometimes, we are Interested in finding the probability that an event will not happen. The complement of an event E, denoted E’,is the set of outcomes in the sample space that are not in E. For example, suppose we are interested in the probability that a horse will lose a race. If event W is the horse winning the race, then the complement of event W is the horse losing the race. To find the probability that the horse loses the race, we need to use the fact that the sum of all probabilities in a probability model must be 1.
P
(
E
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The probability of the horse winning added to the probability of the horse losing must be equal to 1. Therefore, if the probability of the horse winning the race is
1
9
,the probability of the horse losing the race is simply.
Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)
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