Chapter 5 – Probability Rules There are certain rules that apply to probability computation. These are known as addition rules and multiplication rules. Addition Rules There are two addition rules: Special Addition rules for two events General Addition Rules for two events

Special Addition Rules If two events, E1 and E2, are mutually exclusive (both cannot happen at the same time), then P(E1 or E2) = P(E1) + P(E2) 5-1, p.100 ex. Problem 5-1 (p.100), 5-2 (p.100-101)

General Addition Rules If two events are not mutually exclusive, then P(E1 or E2)=P(E1)+P(E2) – P(E1 and E2) formula 5-2, p. 101 ex. Problem 5-3 (p.101-102), 5-5 (p.102) Exercises from book p.104: #3

Multiplication rules Special multiplication rule If two events, A and B, are independent of each other, then P(A and B)=P(A) X P(B) formula 5-5, p.105 ex. 5-7, p.106 Exercises from book p.107: #2, #8

General Multiplication Rule Dependent events If the occurrence of one event affects the probability that another event will or will not occur, then both events are dependent. If A and B are dependent events, then P(A and B)=P(A) • P(B|A) formula 5-6, p.108 Example 5-10, p.109, Exercises from book p.111-112: #3, #5, #8

Probability Functions Random Variable A variable which takes on a value by chance.For example, you are tossing a coin three times. The number of heads that you get is a random variable. How many heads would you get? May be 0, 1, 2, or 3. How many head you actually get depends on chance. Ex.2 You are checking quality of 10 items of a product. The number of defective items is a random variable. This number could be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

Probability Distribution It is a listing of all possible values of a random variable in an experiment and probabilities of all those values. Suppose, we are tossing a coin 3 times. The number of heads is the random variable. Possible values of this random variable are 0, 1, 2, and 3. Probability Distribution looks like this: Values of RV, X Probability 0 1/8 1 3/8 2 3/8 3 1/8

Discrete and Continuous There are two types of probability distributions: Discrete – if the probability distribution is associated with a random variable that takes on only certain specified values, then it is discrete probability distribution.

Continuous Probability distribution Continuous Probability Distribution - If the probability distribution is associated with a random variable that can take on any value, it is a continuous probability distribution. To understand the difference between discrete and continuous probability distributions, look at the following table. For a discrete random variable, only certain specified values are possible (as denoted by points on the scale). For a continuous random variable, any values on the scale are possible.