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all possible outcomes B A D Olo A questions 2 and 3 using this Venn diagram which depicts 4 events A, Figure 1. B, C, and D as circles. Which of the following statements is ALWAYS TRUE? Pr[ A and B ] = Pr[ A ] . Pr[ B] Pr[ A or B or C] = Pr[ A ] • Pr[ B] · Pr[ C] Pr[ C] = 1 - Pr[A] - Pr[B] Pr[ A and B and C] = 1 O Pr[ A or C] = Pr[ A ] + Pr[ C ]

all possible outcomes B A D Olo A questions 2 and 3 using this Venn diagram which depicts 4 events A, Figure 1. B, C, and D as circles. Which of the following statements is ALWAYS TRUE? Pr[ A and B ] = Pr[ A ] . Pr[ B] Pr[ A or B or C] = Pr[ A ] • Pr[ B] · Pr[ C] Pr[ C] = 1 - Pr[A] - Pr[B] Pr[ A and B and C] = 1 O Pr[ A or C] = Pr[ A ] + Pr[ C ]

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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One way to visualize possible events is to depict them in Venn diagram. For example, the diagram below can represent all possible birds observed at West Meadow Beach. Set A corresponds to songbirds (e.g., warblers, finches, sparrows, blackbirds, orioles, etc.), and set B to birds with red on their feathers (e.g., cardinals, red-winged blackbirds, ruby-throated hummingbird, etc.). Many songbirds also have red on their feathers (e.g., cardinals, red-winged blackbirds, robin), but there are birds with red feathers that are not songbirds (e.g., ruby-throated hummingbird). Hence, in this example, the intersection between set A and set B includes songbirds with red, and thus the probability that a bird seen at West Meadow Beach is a songbird with red somewhere on its feathers. We can use these sets to investigate the probability of drawing birds of particular characteristics from the universe of events. For example, the probability of drawing a songbird is represented by set A, while the probability of drawing a bird with red feathers is represented by set B. Set C corresponds to ducks and D corresponds to buffleheads, we can then understand why D is completely included in C: all buffleheads are ducks, but only some ducks are buffleheads. This Venn diagram also shows mutual exclusivity. set A and set C are mutually exclusive: a bird can be a songbird or a duck, but it cannot be both at the same time. When events are mutually exclusive there is no overlap between them and thus their intersection is empty: the probability that a bird seen at West Meadow Beach is both a songbird and a duck is 0. The probability of mutually exclusive events can be added straightaway: the probability that a bird seen at West Meadow Beach is either a songbird or a duck is given by adding A and B.
Transcribed Image Text:One way to visualize possible events is to depict them in Venn diagram. For example, the diagram below can represent all possible birds observed at West Meadow Beach. Set A corresponds to songbirds (e.g., warblers, finches, sparrows, blackbirds, orioles, etc.), and set B to birds with red on their feathers (e.g., cardinals, red-winged blackbirds, ruby-throated hummingbird, etc.). Many songbirds also have red on their feathers (e.g., cardinals, red-winged blackbirds, robin), but there are birds with red feathers that are not songbirds (e.g., ruby-throated hummingbird). Hence, in this example, the intersection between set A and set B includes songbirds with red, and thus the probability that a bird seen at West Meadow Beach is a songbird with red somewhere on its feathers. We can use these sets to investigate the probability of drawing birds of particular characteristics from the universe of events. For example, the probability of drawing a songbird is represented by set A, while the probability of drawing a bird with red feathers is represented by set B. Set C corresponds to ducks and D corresponds to buffleheads, we can then understand why D is completely included in C: all buffleheads are ducks, but only some ducks are buffleheads. This Venn diagram also shows mutual exclusivity. set A and set C are mutually exclusive: a bird can be a songbird or a duck, but it cannot be both at the same time. When events are mutually exclusive there is no overlap between them and thus their intersection is empty: the probability that a bird seen at West Meadow Beach is both a songbird and a duck is 0. The probability of mutually exclusive events can be added straightaway: the probability that a bird seen at West Meadow Beach is either a songbird or a duck is given by adding A and B.
all possible outcomes B с llo e Figure 1. Answer questions 2 and 3 using this Venn diagram which depicts 4 events A, B, C, and D as circles. Which of the following statements is ALWAYS TRUE? O Pr[ A and B ] = Pr[ A ] • Pr[ B] Pr[ A or B or C ] = Pr[ A ] · Pr[ B] · Pr[ C ] Pr[ C ] = 1 - Pr[A] - Pr[B] Pr[ A and B and C] = 1 ○ Pr[ A or C] = Pr[ A ] + Pr[ C ]
Transcribed Image Text:all possible outcomes B с llo e Figure 1. Answer questions 2 and 3 using this Venn diagram which depicts 4 events A, B, C, and D as circles. Which of the following statements is ALWAYS TRUE? O Pr[ A and B ] = Pr[ A ] • Pr[ B] Pr[ A or B or C ] = Pr[ A ] · Pr[ B] · Pr[ C ] Pr[ C ] = 1 - Pr[A] - Pr[B] Pr[ A and B and C] = 1 ○ Pr[ A or C] = Pr[ A ] + Pr[ C ]
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