STATISTICS QUANTITATIVE TECHNIQUES PROBABILITY.pdf
- 1. QUANTITATIVE TECHNIQUES : PROBABILITY NOTES LO1: Discuss the concept “probability”and the reasons why it is important . Probability is the chance that a given event will occur. Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event, and 1 signifies a sure event. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In simple terms, it quantifies the likelihood of an outcome in a given set of circumstances, providing a basis for making informed predictions and decisions in various fields, including mathematics, statistics, and everyday life. Why is it important ? We often use probability assessments informally in our daily lives to plan or make decisions. Formal probability theory is a fundamental tool used by researchers, health- care providers, insurance companies, stockbrokers and many others to make decisions in contexts of uncertainty. Probability provides information about the likelihood that something will happen. Meteorologists, for instance, use weather patterns to predict the probability of rain. In epidemiology, probability theory is used to understand the relationship between exposures and the risk of health effects. LO2: Examine the basic probability concepts , including experiments, sample spaces, possible outcomes and events : a) By a statistical experiment we mean the procedure of drawing a sample with the intention of making a decision. The sample values are to be regarded as the values of a random variable defined on some meas urable space, and the decisions made are to be functions of this random variable. b) Sample spaces: is the set of all possible outcomes of a statistical experiment, and it is sometimes referred to as a probability space. c) outcomes are observations of the experiment, and they are sometimes referred to as sample points.
- 2. d) An event is a subset of a sample space LO3: Properties of probability
- 3. LO4: Distinguish between events that are mutually exclusive and events that are not mutually exclusive: i) Two events are called mutually exclusive if they cannot happen at the same time. In other words, two mutually exclusive events do not intersect, however Two events A and B are called non-mutually exclusive if their intersection is not zero. In other words, two non-mutually exclusive events can happen at the same time ii) LO5: Distinguish between dependent and independent events: Two events are independent if the probability of the second event is not affected by the outcome of the first event. If, instead, the outcome of the first event does affect the probability of the second event, these events are dependent. Examples of independent events: o flipping a coin and rolling a die o flipping a coin or rolling a die twice o choosing a card from a deck, replacing it, shuffling, and choosing again o choosing a particular pair of shoes and the weather in Sweden Examples of dependent events: o choosing a card from a deck and then choosing another without putting the first card back in the deck o picking two marbles from a bag that contains ten black marbles and ten white marbles without putting either marble back in the bag o what I choose to eat for lunch and whether I am hungry by three o’clock
- 4. LO6: Apply the addition and multiplication rules to calculate probabilities