Applied Probability and Statistics - C955 - Module 7: Probability with Complete Solutions 2023(GRADED A+)

random experiment - ANSWER-Experiment in which the outcome is not known ahead of time and in which results do not affect future outcomes. sample size - ANSWER-The number of different outcomes for an experiment. intersection - ANSWER-The intersection of A and B will have all elements that are in both A and B. You can think of an intersection as 'A and B,' since it contains an element if it is in A and in B. The intersection of many sets will have an element if it appears in all of the sets.. theoretical probability - ANSWER-Also called the Actual, Exact, or Classical Probability, it is computed by dividing the number of outcomes where the desired event occurs by the total number of outcomes. Note that the outcomes must be equally likely. multiplication rule for independent events - ANSWER-If two events are independent, then P(A and B) = P(A) x P(B). fair - ANSWER-An experiment in which all outcomes are equally likely. relative frequency - ANSWER-A way to approximate a probability by taking the number of times an event occurs divided by the total number of trials. disjoint - ANSWER-Two events which cannot both occur at the same time. frequency table - ANSWER-A table which records the frequency of instances in different categories. It can be used to determine if the categories are dependent or independent. experiment - ANSWER-A procedure that can be done repeatedly which has a well defined set of outcomes. independent events - ANSWER-Events, where the occurrence of one does not affect the probability that the other event(s) will occur. the law of large numbers - ANSWER-As the number of trials increases the empirical probability converges on the theoretical probability, that is the estimate of the true probability becomes more accurate.