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# Pre-Cal 40S Slides May 23, 2008

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More on independence and dependence, discussion of mutually exclusive events.

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### Pre-Cal 40S Slides May 23, 2008

1. 1. Risk is when an outcome’s probability is known. Uncertainty is when an outcome’s probability is unknown.
2. 2. ` Phone Numbers A computer is used to generate random telephone numbers. Of the numbers generated and in service, 56 are unlisted and 144 are listed in the telephone directory. If one of these telephone numbers is randomly selected, what is the probability that it is unlisted?
3. 3. The probability that Gallant Fox will win the ﬁrst race is 2/5 and that Nashau will win the second race is 1/3. 1. What is the probability that both horses will win their respective races? 2. What is the probability that both horses will lose their respective races? 3. What is the probability that at least one horse will win a race?
4. 4. Chad has arranged to meet his girlfriend, Stephanie, either in the library or in the student lounge. The probability that he meets her in the lounge is 1/3, and the probability that he meets her in the library is 2/9. a. What is the probability that he meets her in the library or lounge? b. What is the probability that he does not meet her at all?
5. 5. Mutually Exclusive Events ... Two events are mutually exclusive (or disjoint) if it is impossible for them to occur together. Formally, two events A and B are mutually exclusive if and only if Not Mutually Exclusive Mutually Exclusive Examples: 1. Experiment: Rolling a die once Sample space S = {1,2,3,4,5,6} Events A = 'observe an odd number' = {1,3,5} B = 'observe an even number' = {2,4,6} A B = (the empty set), so A and B are mutually exclusive.
6. 6. Mutually Exclusive Events ... Two events are mutually exclusive (or disjoint) if it is impossible for them to occur together. Formally, two events A and B are mutually exclusive if and only if Not Mutually Exclusive Mutually Exclusive Examples: 1. Experiment: Rolling a die once Sample space S = {1,2,3,4,5,6} Events A = 'observe an odd number' = {1,3,5} B = 'observe an even number' = {2,4,6} A B = (the empty set), so A and B are mutually exclusive. 2. A subject in a study cannot be both male and female, nor can they be aged 20 and 30. A subject could however be both male and 20, or both female and 30.
7. 7. Example Suppose we wish to ﬁnd the probability of drawing either a king or a spade in a single draw from a pack of 52 playing cards. We deﬁne the events A = 'draw a king' and B = 'draw a spade' Since there are 4 kings in the pack and 13 spades, but 1 card is both a king and a spade, we have: P(A U B) = P(A) + P(B) - P(A B) = 4/52 + 13/52 - 1/52 = 16/52 So, the probability of drawing either a king or a spade is 16/52 = 4/13.
8. 8. Identify the events as: mutually exclusive dependent Drag'n Drop not mutually exclusive independent Baby! a. A bag contains four red and seven black marbles. The event is randomly selecting a red marble from the bag, returning it to the bag, and then randomly selecting another red marble from the bag. mutually exclusive independent b. One card - a red card or a king - is randomly drawn from a deck of cards. not mutually exclusive independent c. A class president and a class treasurer are randomly selected from a group of 16 students. mutually exclusive dependent d. One card - a red king or a black queen - is randomly drawn from a deck of cards. mutually exclusive independent e. Rolling two dice and getting an even sum or a double.