University:
Kentucky State University
Course:
MAT 321 | Probability/Statistics I
Academic year:

2023
Views:

146

Pages:

5
Author:

diamundgalx45p

Probability of single event • Probability (P) is the measure of the likelihood that an event will occur. P = Favorable outcome Sum of all possible outcomes E.g.1. Tossing a coin: 2 possible out comes: head/tail. The probability of head =probability of tail = ½, 0.5 or 50%. E.g.2. Throwing six sided die: 6 possible outcomes with probability for each of 1/6. • The probability of an event (Ei) is written as P(Ei). • Probability is quantified as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility and 1 indicates certainty (no negative probability). P ( Ei )  0 • The sum of probabilities of the mutually exclusive (can not occur at the same time) outcomes is equal to 1: P( E1 ) + P( E2 ) + P( E3 ) + ...............P( En ) = 1 Marginal probability • A marginal probability is a probability in which the numerator of the probability is a marginal total from a table as relative frequency. E.g. subjects (N = 100) were categorized as underweight (n=15), normal weight (=77) and overweight (n=8). P for randomly choosing underweight subject = n/N = 15/100 = 0.15. Probability of single event • Complimentary events: - The probability of an event A NOT occurring (opposite or compliment of A) is P(Ā) – The probability of an event A is equal to 1 minus the probability of its compliment which is written as Ā, and P(Ā)=1-P(A) E.g. the probability of not having 1 upon throwing a dice = 1(1/6)=5/6 Probability of two or (∩) more independent events (not mutually exclusive or joint) -Joint probability If two independent events A and B can occur on a single performance of an experiment (not mutually exclusive) , this is called the intersection or joint probability of A and B, denoted as P(A∩B) or P(A and B) and is given as. P(A∩B)=P(A)P(B),this is called multiplication rule • If the probability of rolling one on the first die is P(1) and the probability of rolling a six on the second die P(6), we can use the formula. Having one for the first die wont affect having 6 for the second (independent) P(1∩6) = P(1) * P(6) = 1/6 *1/6 =1/36 • A drug is known to be 80% effective in curing a certain disease. Suppose that 3 patients with the disease are to be given the drug, what is the probability that the three patients are cured (C) : three independent and joint events P(C,C∩C) = 0.8*0.8*0.8 =0.512 what is the probability that the three patients fail to be cured (F) P(F,F∩F) = 0.2*0.2*0.2 =0.008 Probability of two independent events (mutually exclusive, disjoint) • Two events are said to be mutually exclusive if they can not occur simultaneously. E.g. when a coin is tossed, it can land head or tail but not both. • For such events P(A∩B)= 0 • For events A OR B to occur: P(A∪B)=P(A)+P(B) • E.g. What is the probability of having 3 or 5 when a dice is rolled: P(A∪B)= 1/6+1/6 =2/6 • A drug is known to be 80% effective in curing a certain disease. Suppose that 3 patients with the disease are to be given the drug, what is the probability that the three patients are cured (All C) or they all fail to be cured (All F) CCC (3 joint) or FFF (3 joint), but both are disjoint P(All C ∪ All F) = 0.512 + 0.008 = 0.52

Probability of Single Event

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