UPSC CSAT || PROBABAILITY || PYQ Analysis 2011-23 || Lecture 32 || Gaurav Nagar Sir || THECOREIAS скачать в хорошем качестве

UPSC CSAT || PROBABAILITY || PYQ Analysis 2011-23 || Lecture 32 || Gaurav Nagar Sir || THECOREIAS

Probability Probability defines the likelihood of occurrence of an event. There are many real-life situations in which we may have to predict the outcome of an event. We may be sure or not sure of the results of an event. In such cases, we say that there is a probability of this event to occur or not occur. Probability generally has great applications in games, in business to make predictions, and also it has extensive applications in this new area of artificial intelligence. The probability of an event can be calculated by the probability formula by simply dividing the favourable number of outcomes by the total number of possible outcomes. The value of the probability of an event happening can lie between 0 and 1 because the favourable number of outcomes can never be more than the total number of outcomes. Also, the favorable number of outcomes cannot be negative. Let us discuss the basics of probability in detail in the following sections. What is Probability? Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows. Probability(Event) = Favorable Outcomes/Total Outcomes = x/n Probability is used to predict the outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards. The probability is classified into two types: Theoretical probability Experimental probability To understand each of these types, click on the respective links. Terminology of Probability Theory Experiment: A trial or an operation conducted to produce an outcome is called an experiment. Sample Space: All the possible outcomes of an experiment together constitute a sample space. For example, the sample space of tossing a coin is {head, tail}. Favorable Outcome: An event that has produced the desired result or expected event is called a favorable outcome. For example, when we roll two dice, the possible/favorable outcomes of getting the sum of numbers on the two dice as 4 are (1,3), (2,2), and (3,1). Trial: A trial denotes doing a random experiment. Random Experiment: An experiment that has a well-defined set of outcomes is called a random experiment. For example, when we toss a coin, we know that we would get ahead or tail, but we are not sure which one will appear. Event: The total number of outcomes of a random experiment is called an event. Equally Likely Events: Events that have the same chances or probability of occurring are called equally likely events. The outcome of one event is independent of the other. For example, when we toss a coin, there are equal chances of getting a head or a tail. Exhaustive Events: When the set of all outcomes of an event is equal to the sample space, we call it an exhaustive event. Mutually Exclusive Events: Events that cannot happen simultaneously are called mutually exclusive events. For example, the climate can be either hot or cold. We cannot experience the same weather simultaneously. Events in Probability In probability theory, an event is a set of outcomes of an experiment or a subset of the sample space. If P(E) represents the probability of an event E, then, we have, P(E) = 0 if and only if E is an impossible event. P(E) = 1 if and only if E is a certain event. 0 ≤ P(E) ≤ 1. P(E) = n(E)/n(S) P(E’) = (n(S) - n(E))/n(S) = 1 - (n(E)/n(S)) E’ represents that the event will not occur. Therefore, now we can also conclude that, P(E) + P(E’) = 1 #barchart #thecoreias #csat #prelims2024 #probability #gauravnagar #upscprelims #upsccsat #upsccsat2023 Complete playlist of CSAT PYQ SERIES    • CSAT PYQ Series 2011-23 Quantitative Aptit...   for Handwriting solution of these PYQ visit our website at https://thecoreias.com/ for more information. . . ➤ Subscribe to our YouTube channel: /@THECOREIAS ➤ Join our Telegram group: https://t.me/THECOREIAS ➤ Explore our courses: https://thecoreias.com/ ➤ Contact us at 011-41008973, 8800141518 or email thecore.org.in@gmail.com Don't forget to visit our website at https://thecoreias.com/ for more information Follow us on social media: Instagram:   / thecoreias   Facebook:   / thecoredelhi   Don't forget to visit our website at https://thecoreias.com/ for more information. Follow us on social media: Instagram:   / thecoreias   Facebook:   / thecoredelhi