By Marcel B. Finan
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Extra resources for A Probability Course for the Actuaries: A Preparation for Exam P 1
4 A club has 10 members. In how many ways can the club choose a president and vice-president if everyone is eligible? 5 In a medical study, patients are classified according to whether they have blood type A, B, AB, or O, and also according to whether their blood pressure is low (L), normal (N), or high (H). Use a tree diagram to represent the various outcomes that can occur. 6 If a travel agency offers special weekend trips to 12 different cities, by air, rail, or bus, in how many different ways can such a trip be arranged?
Since S = E ∪ E c and E ∩ E c = ∅, P (S) = P (E) + P (E c ). Thus, P (E c ) = 1 − P (E). 45. What is the probability that a college student without the flu shot will not get the flu? Solution. Our sample space consists of those students who did not get the flu shot. Let E be the set of those students without the flu shot who did get the flu. 45. 55 The union of two events A and B is the event A ∪ B whose outcomes are either in A or in B. The intersection of two events A and B is the event A ∩ B whose outcomes are outcomes of both events A and B.
For the kth kind we have n−n1 −n2 −· · ·−nk−1 slots and nk objects to place such that the order is unimportant. There are C(n − n1 − n2 − · · · − nk−1 , nk ) different ways. Thus, applying the Fundamental Principle of Counting we find that the number of distinguishable permutations is n! n2 ! · · · nk ! 48 COUNTING AND COMBINATORICS It follows that the number of different rearrangements of the letters in DE8! = 3360. 3! 1 In how many ways can you arrange 2 red, 3 green, and 5 blue balls in a row?