Statistics Probability

University:
Bradley University
Course:
MTH 325 | Probability and Statistics I
Academic year:

2022
Views:

293

Pages:

2
Author:

Killian Mata

PROBABILITY BASIC PROBABILITY The measure of the likelihood that a specific event will occur in a random experiment. Probability is quantified as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. THE MULTIPLICATION RULE To find the probability of two events happening at the same time (this is also one of the AP Statistics formulas), you can use the general multiplication rule formula. The formula is = P(A ∩ B) = P(A) P(B|A) and the specific multiplication rule is P(A and B) = P(A) * P(B) Example - If the probability of event A is 2/9 and the probability of event B is 3/9 then the probability of both events happening at the same time is (2/9)*(3/9) = 6/81 = 2/27. THE ADDITION RULE States the probability of two events is the sum of the probability that either will happen minus the probability that both will happen. Example - When two events, A and B, are non-mutually exclusive, there is some overlap between these events. The probability that A or B will occur is the sum of the probability of each event, minus the probability of the overlap. P(A or B) = P(A) + P(B) - P(A and B) PERMUTATIONS & COMBINATIONS A combination is a selection of all or part of a set of objects, with no regard to the order in which objects are selected. Suppose we have a set of three letters: A, B, and C. From this set, we may ask how many different ways we can select 2 letters from that set. Example - Choosing 3 desserts from a menu of 10. C(10,3) = 120. Permutation: Listing your 3 favorite desserts, in order, from a menu of 10. P(10,3) = 720. A permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement. Suppose we have a set of three letters: A, B, and C. We may ask how many different ways we can arrange 2 letters from that set. Example - suppose we have a set of three letters: A, B, and C. We might ask how many ways we can arrange 2 letters from that set. Each possible arrangement would be an example of a permutation. The complete list of possible permutations would be: AB, AC, BA, BC, CA, and CB.