By Marcel B. Finan
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Extra resources for A Probability Course for the Actuaries: A Preparation for Exam P 1
A) Find the sample space of this experiment. (b) Find the event of rolling the die an even number. 2 An experiment consists of the following two stages: (1) first a fair die is rolled (2) if the number appearing is even, then a fair coin is tossed; if the number appearing is odd, then the die is tossed again. An outcome of this experiment is a pair of the form (outcome from stage 1, outcome from stage 2). Let S be the collection of all outcomes. Find the sample space of this experiment. 3 ‡ An insurer offers a health plan to the employees of a large company.
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?
Clearly, P (S) = 1. 3 (b). 4 A hand of 5 cards is dealt from a deck. Let E be the event that the hand contains 5 aces. List the elements of E. Solution. Recall that a standard deck of 52 playing cards can be described as follows: hearts (red) Ace clubs (black) Ace diamonds (red) Ace spades (black) Ace 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 Jack Jack Jack Jack Queen Queen Queen Queen King King King King Cards labeled Ace, Jack, Queen, or King are called face cards.
A Probability Course for the Actuaries: A Preparation for Exam P 1 by Marcel B. Finan