By Marcel B. Finan
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This best-selling engineering information textual content offers a pragmatic technique that's extra orientated to engineering and the chemical and actual sciences than many related texts. It's filled with distinctive challenge units that mirror life like occasions engineers will stumble upon of their operating lives.
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Additional info for A Probability Course for the Actuaries: A Preparation for Exam P 1
1 Consider the random experiment of rolling a die. (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.
Then there are 5 ways to fill the first spot, 4 ways to fill the third, 3 to fill the fourth, and so on. There are 5! 3 Five different books are on a shelf. In how many different ways could you arrange them? Solution. The five books can be arranged in 5 · 4 · 3 · 2 · 1 = 5! = 120 ways Counting Permutations We next consider the permutations of a set of objects taken from a larger set. Suppose we have n items. How many ordered arrangements of k items can we form from these n items? The number of permutations is denoted by P (n, k).
6 What is the probability of rolling a 3 or a 4 with a fair die? Solution. 7 In a room containing n people, calculate the chance that at least two of them have the same birthday. Solution. We have P(Two or more have birthday match) = 1 - P(no birthday match) Since each person was born on one of the 365 days in the year, there are (365)n possible outcomes (assuming no one was born in Feb 29). 5 It is important to keep in mind that the above definition of probability applies only to a sample space that has equally likely outcomes.