Solution i P Rahim 20 5 1 ii PKamal Rahim PKamal PRahim 40 5 2 5 1 5 1 Random

# Solution i p rahim 20 5 1 ii pkamal rahim pkamal

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Solution (i) P (Rahim) = 20 . 0 5 1 (ii) P(Kamal Rahim) = P(Kamal)+ P(Rahim) 40 . 0 5 2 5 1 5 1 Random variable A random variable is a variable whose value cannot be exactly predicted on any particular occasion. More precisely, a random variable must have a range or set of possible values and a definable probability associated with each value. Example A coin is tossed twice. What is the number of success? Solution: Let us represent the number of success by x which can assume the values 0, 1, and 2. the sample space of this experiment is: SS, SF, FS, FF, where S and F denote successes and failure respectively in the two trials. Table below shows the values of x i and the corresponding probabilities f (x i ) . i x 0 1 2 i x f ¼ ½ ¼ 5

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The probability that x will assume the value 1 is the sum of the probabilities for the sample points FS and SF Example Consider the experiment of rolling a die twice. Find the probability that the sum of the numbers obtained on two rolls is 5, 7, or 10. Solution (i) 11111 . 9 1 36 4 P (ii) 16666 . 0 6 1 36 6 P (iii) 0833 . 0 12 1 36 3 P Example Assume that during the last calendar year there were 500 births at a local hospital. 320 of them were baby girls. Find the probability that the next birth (or any randomly selected birth) is a girl. Solution 500 320 ) ( births girl of Number Total year last born girl of Number Girl P 6
Example: A machine fills plastic bags with a mixture of beans, broccoli and other vegetables. Most of the bags contain the correct weight, but because of the slight variation in the size of the beans and other vegetables, a package might be slightly underweight or overweight. A check of 4,000 packages in the past revealed: Weight Event Number of packages Underweight A 100 Satisfactory B 3600 Overweight C 300 What is the probability that a particular package will be either underweight or overweight? Solution Here the events are mutually exclusive, meaning that a package of mixed vegetables cannot be underweight, satisfactory and overweight at the same time. The outcome `underweight’ is the event . A The outcome `overweight’ is the event . C Weight Event Number of packages Probability of occurrence Underweight A 100 025 . 4000 100 Satisfactory B 3600 .900 Overweight C 300 .075 4000 1.000 Applying the special rule of addition: 10 . 0 075 . 0 025 . 0 ) ( ) ( ) ( ) ( C P A P C A P C or A P Marginal and Conditional Probabilities 7

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Suppose all 100 employees of a company were asked whether they are in favor or against paying high salaries to CEOs of U.S. companies, Table-A below gives a two-way classification of the responses of these 100 employees. Assume that every employee responds either in favor or against.

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