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

This preview shows page 5 - 9 out of 13 pages.

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
Image of page 5

Subscribe to view the full document.

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
Image of page 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
Image of page 7

Subscribe to view the full document.

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.
Image of page 8
Image of page 9

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes