Basic probability, Introduction to probabability and its overview

what probability really means. Probability is simply how likely something is to happen. [music] It answers everyday questions like, "Will it rain today? Will I pass the exam? [music] Will my bus arrive early or late? Think of it as a chance meter that goes from impossible cannot happen at all. uncertain, might happen, certain [music] definitely will happen. Life is full of uncertainty and probability helps us reason about uncertainty instead of guessing blindly. Forms of probability. [music] Ways we understand chance. One, theoretical probability. Knowing chances [music] before anything happens. Imagine you put one red [music] pen and one blue pen inside your bag. You close the [music] bag, mix them, and pick one without looking. Before you even put your hand inside, you already know something important. There are only two possible outcomes. [music] You either pick the red pen or the blue pen. Nothing [music] else can come out because only two pens exist. Now think about [music] fairness. Both pens are the same size, same shape, and equally [music] reachable. That means neither pen has an advantage. So in your mind, the chance of [music] picking red feels exactly the same as picking blue. You didn't need to try it many times. You didn't need experience. You just use logic and known possibilities. That is theoretical probability. Predicting chance by understanding the situation before it happen. Real life version. When a university announces that half of applicants are admitted, any [music] single applicant logically has a moderate chance of admission. You reason using known information, [music] not past personal experience. Two, experimental probability, [music] learning from repeated experience. Now, picture your daily routine in Campala. You leave [music] home at 7:30 a.m. to go to campus. During one week, this is what happens. Monday late, [music] Tuesday late, Wednesday early, Thursday late, Friday early. After observing this pattern, you begin to form a belief. When I leave at 7:30, I am usually late. Notice something important. You did not predict this before trying. You discovered the likelihood by observing real outcomes. [music] This is exactly how businesses operate. For example, [music] at a bank like where you work at Absa, managers observe how many borrowers repay loans on time. Over time, they see patterns and [music] estimate the likelihood of default. Based on experience, experimental probability is basically life teaching you patterns through repetition. Three, [music] subjective probability belief based on knowledge and [music] judgment. Suppose you have a CPA paper coming up. You revised thoroughly, [music] practiced past papers and attended discussions. Because of that preparation, you tell yourself, I believe I will pass. You are not using statistics. You are not counting outcomes. You are making a judgment based on knowledge of your preparation level. Another [music] student who did not revise might believe they will [music] fail. Both of you are making probability judgments but [music] based on personal assessment. This is extremely common in [music] leadership and management. When a manager predicts whether a new business idea will succeed, they rely on experience, insight, and understanding of the market. Subjective probability is [music] educated belief about chance. Four, simple event, [music] one clear outcome. Imagine a lecturer asks one question in class and [music] calls your name. Two things could happen. You answer correctly. You answer incorrectly. But the event we are focusing on is only one. You answer correctly. That single [music] outcome is a simple event. Another everyday example. You receive one phone call and check [music] who is calling. The event is it is my friend calling. Only one outcome [music] matters. Not many combined outcomes. Simple events are [music] straightforward. One action, one result. Five. Compound event. Several possible outcomes grouped together. Now think about breakfast [music] at a campus cafeteria. You ask the server for a hot drink. They tell you [music] today they only have tea or coffee. You say I will take to coffee. Any is fine. [music] You are not focusing on one outcome. You accept multiple possibilities together. That makes [music] it a compound event. Another realistic example from business. A company hopes to make [music] profit this quarter from either product A or [music] product B. Success can come from more than one outcome. Compound events are [music] about combined possibilities. Six. Certain events guaranteed to happen. Think about time passing. No matter what you do today, tomorrow will come. You cannot stop it. Or think about university life. If you enroll in a semester, exams will eventually occur. It is part of the system. These events require no guessing. [music] They will happen with full certainty. Probability here simply recognizes inevitability. Some outcomes are guaranteed in life. Seven. Impossible event cannot occur in reality. Imagine [music] a student claiming they scored 105% in an exam. That cannot happen because exam scores have a maximum limit. Or [music] imagine someone saying February will have 35 days to year that contradicts [music] the structure of the calendar. Impossible events violate the rules of the system they exist [music] in. In probability thinking, recognizing impossibility [music] is just as important as recognizing certainty. [music] It helps eliminate unrealistic expectations. Eight complimentary events. One must happen if the other does not. Picture results. [music] Day for any student only two outcomes exist. pass fail. If you do not pass, you automatically fail. If you do not fail, you automatically pass. The two outcomes cover every [music] possibility together. Another example from business finance. A customer either repays a loan or does not repay. There is no third option. Complimentary events are like two [music] sides of one coin. One fills the gap left by the other. Nine independent events [music] no influence between outcomes. Suppose two different students in different rooms sit for separate exams. Whether student passes does not affect student B's performance. Each result [music] stands alone. Or imagine you toss a coin today and toss another coin tomorrow. Tomorrow's outcome does not remember yesterday's [music] outcome. Independence means no connection, [music] no influence, no carryover effect. This idea is important in auditing and research because we must know whether events truly affect each [music] other. 10. Dependent events. One outcome [music] changes another. Now think about studying. If you study consistently, your chance of passing increases. If [music] you skip revision, your chance of failing increases. The second outcome depends on the first action. Another [music] example from daily life. If it rains heavily in Kala, traffic [music] becomes worse. Rain influences traffic conditions. [music] In finance, if a company earns high profit, it is more likely to expand [music] operations. Dependent events show cause and effect [music] relationships. The big picture to hold in your mind. Probability is not about numbers first. It is about understanding [music] situations involving uncertainty. Whenever you [music] face a situation, you can ask what outcomes are possible. Do outcomes influence each other or not? Is this based on logic, experience or judgment? [music] Is the outcome certain, impossible or uncertain? Once you answer those questions, you are already thinking [music] probabilistically.