Fine friends, lecture 24 is about the basic probability concepts. The concept that we are going to discuss is about the terminologies such as independence, mutually exclusive events, multiplication rule, etc. In previous lecture, we discussed that sample statistics mean and standard deviation can be used to draw conclusions about a population parameters. But, conclusions cannot be hundred percent right there is always risk associated with this conclusions this Risk is referred to as probability of concluding things rightly. in day to day conversation, we often see or hear, probably, it may rain today, chances of dodges and Braves winning the baseball match are equal. When we say probable or chance, it indicates degree of uncertainty.

Statistical methods are largely based on probability theories. We draw conclusions about population using probability distributions. That's all fine. But for the above stated purpose, we need to answer understand some of the basic terminologies of probability. Let us learn what is a random experiment. A random experiment is an action or process that leads to one of several possible outcomes.

Note the two words that I have uttered right now, the experiment and outcome that is understand them with some situations, let's say an experiment as flipping a coin. Now, what are the possible outcome for this experiment? Either head or Am I right? What about the experiment of tossing a die? The possible outcome could be 12345 or six. Now consider the example that you are regarding the grades of MBA students.

What would be the possible outcome? The grades such as a, b, c or d, etc. Similarly, consider the experiment of sorting products during a quality inspection. The possible outcome would be passed or failed product What about flipping two coins simultaneously? The possible outcome could be both heads. A head first, followed by a tail, a tail first, followed by a head and both tails.

Now, collection of all possible outcomes are called sample set. Let us move to the next terminology. The event event is a collection or set off one or more simple events from the list of all possible outcome. mutually exclusive events and event is mutually exclusive when no two outcomes could occur at the same time What could be the examples? Well take the example of flipping a coin while flipping a coin, you cannot have a head and a tail. At the same time it will be either head or tail, but not both.

Hence, this event is known as mutually exclusive events. Similarly, when sorting products during inspection, one product cannot be passed, as well as failed at the same time, the product would be in a category of either failed or passed, but not both. Hence, this is known as mutually exclusive Live Events are calculating the probability we can use the classical method. classic definition of probability says if an event say a can occur in Emrys out of a possible and equally likely ways, then probability of occurring event A that is P of A is equals to m divided by n. example. Suppose a god is randomly selected from a standard 52 card deck. What is the probability that selected card is club card answer there are 13 clubs in a pack of card.

That means, there are 13 possible ways m out of 52 equally likely Ways and Means, probability of selected card being a club card fee of clubs is equals to m by n or 13 divided by 52 is equal to 0.25. Similar to the mutually exclusive concept, there is one more concept of basic probability known as dependent events to events are set to be independent when the probability of one event is not affected by the occurrence of other event. addition rule of probability is different from mutually exclusive and not mutually exclusive events. For mutually exclusive events B of A or B is equals to P of A plus B of B. For example, draw a card from 52 card deck probability of the card, either being spade or club solution. We Have spayed is equals to 13 oblique 52 and P club is equals to 13 oblique 52 then P spade our club is equals to 13 oblique 52 plus 13 oblique 52 is equals to 26 oblique 52 because p spade and P of club are mutually exclusive events, as both cannot happen together.

Addition rule of probability is different from mutually exclusive and not mutually exclusive events are not mutually exclusive. Events B of A or B is equals to P of A plus B of b minus P of A and B. Example, draw a card from 52 card deck probability of the card either being queen or club solution, we have queen is equals to four public 52 and P of club is equals to 13 object 52. Now, these events are not mutually exclusive, because the card drawn could be P of Queen or b p of club at the same time tense Queen or club is equals to p of Queen plus p of club minus p of Queen and club matters for public 52 plus protein or black 52 minus one divided by 52 is equal to 16 divided by 52. Similarly, the multiplication rule of probability for two independent events P of A and P is equals to P of A into P of B for two dependent events.

We are Have a and b is equals to P of A into P of B given A where P of A given B is known as probability of event B given occurrence of event A. This is also called conditional probability. conditional probability P of B given A is equals to P of A and B divided by B of B. With this, we conclude the basic of probability, a greenbelt we'll be working under the black belt, while undertaking Six Sigma projects and They need to understand only the basic concepts of probability. However, these concepts are more elaborated in our blackbelt course. Well, it's time to move forward with the next lecture on collecting data based on the blk three C. Thank you.