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Download A Probability Course for the Actuaries: A Preparation for by Marcel B. Finan PDF

By Marcel B. Finan

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Example text

An event is a subset of the sample space. For example, the event of rolling an odd number with a die consists of three simple events {1, 3, 5}. 1 Consider the random experiment of tossing a coin three times. 57 58 PROBABILITY: DEFINITIONS AND PROPERTIES (a) Find the sample space of this experiment. (b) Find the outcomes of the event of obtaining more than one head. Solution. We will use T for tail and H for head. (a) The sample space is composed of eight simple events: S = {T T T, T T H, T HT, T HH, HT T, HT H, HHT, HHH}.

3 You are taking 3 shirts(red, blue, yellow) and 2 pairs of pants (tan, gray) on a trip. How many different choices of outfits do you have? 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.

Two events A and B are said to be mutually exclusive if they have no outcomes in common. In this case A ∩ B = ∅ and P (A ∩ B) = P (∅) = 0. 2 Consider the sample space of rolling a die. Let A be the event of rolling an even number, B the event of rolling an odd number, and C the event of rolling a 2. Find (a) A ∪ B, A ∪ C, and B ∪ C. (b) A ∩ B, A ∩ C, and B ∩ C. (c) Which events are mutually exclusive? Solution.

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