Addition And Multiplication Theorem Of Probability Pdf

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addition and multiplication theorem of probability pdf

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A probability gives the likelihood that a defined event will occur. It is quantified as a positive number between 0 the event is impossible and 1 the event is certain.

We have studied what probability is and how it can be measured. We dealt with simple problems. Now we shall consider some of the laws of probability to tackle complex situation.

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The probability of happening an event can easily be found using the definition of probability. But just the definition cannot be used to find the probability of happening at least one of the given events. The event of getting 2 heads, A and the event of getting 2 tails, B when two coins are tossed are mutually exclusive. Two events are said to be mutually exhaustive if there is a certainty of occurring at least one of those two events. If A and B are two mutually exhaustive then the probability of their union is 1.

Problem 1 :. Solution :. Problem 2 :. First let us find the value of P B , for that let use the formula for addition theorem on probability. Problem 3 :. A die is thrown twice.

Statistics - Probability Multiplicative Theorem

If A and B are two events in a probability experiment, then the probability that either one of the events will occur is:. This can be represented in a Venn diagram as:. If you take out a single card from a regular pack of cards, what is probability that the card is either an ace or spade? Let X be the event of picking an ace and Y be the event of picking a spade. The two events are not mutually exclusive, as there is one favorable outcome in which the card can be both an ace and spade.

The probability of event A or event B can be found by adding the probability of the separate events A and B and subtracting any intersection of the two events.

Addition Rules for Probability

We need a rule to guide us. What is the probability of landing on red or blue after spinning this spinner? If a single marble is chosen at random from the jar, what is the probability that it is yellow or green? In each of the three experiments above, the events are mutually exclusive. Let's look at some experiments in which the events are non-mutually exclusive.

Basic Probability Rules

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.


In the previous section, we introduced probability as a way to quantify the uncertainty that arises from conducting experiments using a random sample from the population of interest. We saw that the probability of an event for example, the event that a randomly chosen person has blood type O can be estimated by the relative frequency with which the event occurs in a long series of trials. So we would collect data from lots of individuals to estimate the probability of someone having blood type O. In this section, we will establish the basic methods and principles for finding probabilities of events. We will also cover some of the basic rules of probability which can be used to calculate probabilities. Since heads and tails are equally likely for each toss in this scenario, each of the possibilities which can result from three tosses will also be equally likely so that we can list all possible values and use this list to calculate probabilities. Since our focus in this course is on data and statistics not theoretical probability , in most of our future problems we will use a summarized dataset, usually a frequency table or two-way table, to calculate probabilities.

The addition rule states the probability of two events is the sum of the probability that either will happen minus the probability that both will happen. The addition rule is summarized by the formula:. Consider the following example. The addition law then simplifies to:.


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