All in One

The Multiplication Rules and Conditional Probability Multiplication Rules: Objective: Find the probability of compound events using multiplication rules. The multiplication rules can be used to find the probability of two or more events   that occur in sequence. For example, if a coin is tossed then a die is rolled, one can find the probability of getting a head on the coin and a 4 on the die. These  two events are said to be independent since the outcome  of the first event (tossing a coin) does not affect the probability outcome of  the second event (rolling a die) ********************************************************************************* Two events A and B are independent if the fact that A occurs does not affect the probability of  B occurring ********************************************************************************* Here are other examples of independent events: Rolling a die and getting a 6, and then rolling a second die and getting a 3. Drawing a

Addition Rules for probability Objective: Find the probability of compound events using the addition rules. Many problems involve finding the probability of two or more events. For example,at a large połitical gathering, one might wish to know, for a person selected at random, the probability that a person is female or a  Republican. In this case, there are three possibilities to consider:  1. The person is a female.  2. The person is a Republican.  3. The person is both a female and a Republican.  Consider another example.  At the same gathering there are Republicans, Democrats, and Independents. If a person is selected at random, what is the  probability that the person is a Democrat or an Independent? in this case, there are only two possibilities: 1. The person is a Democrat. 2. The person is an Independent. The difference between the two examples is that in the first case, the person selectedcan be a female and a Republican at

Complementary Events:     Another important concept in probability theory is that of complementary events. When is die is  rolled, for instance, the sample space consists outcomes 1, 2, 3, 4, 5, and 6. The event E of getting odd numbers consists of the outcomes I, 3, and 5. The event of not getting odd  numbers  is called the complement of event E and it consists of outcomes 2,4, and 6. The complement of an event E is the set of outcomes in the sample space  that are not included in the outcomes of event E. The complernent of E is denoted by  E̅   (read "E bar) Further illustrates the concept of complementary events through example. Find the complement of each event. a. Rolling a die and getting a 4. b. Selecting a letter of the alphabet and getting a vowel. C. Selecting a month and getting a month that begins with a J. d. Selecting a day of the week and getting a weekday. Solution a.     S={1,2,3,4,5,6}        Complement of 4 is        Getting a 1, 2, 3, 5,

     Probability:                     Probability as a general concept can be defined as the chance of an event occurring. Many people are familiar with probability from observing or playing games of chance, such as card games, slot machines, or lotteries. In addition to being used in games of chance, probability theory is used in the fields of insurance, investments, and weather forecasting, and in various other areas.                  Probability is the basis of inferential statistics. For example, predictions are based on probability, and hypotheses are tested by using probability.        The basic concepts of probability are explained in this lecture. These concepts in-clude probability experiments, sample spaces, the addition and multiplication rules, and the probabilities of complementary events. The theory of probability grew out of the study of various games of chance using coins, dice, and cards. Since these devices lend themselves well to the application of concepts