11. Given two events, A and B. Find the following if P(A)=0.7, P(B)=0.5, and P(A U B)=0.9.Complete a Venn diagram before answering.(a) P(ANB)(b) P((AUB)')(c) P(A/B)

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Answered: 1. Given two events, A and B. Find the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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…
1. Two coins are tossed. What is the conditional probability that the two heads result, given that there is at least one head? 2. Given P(A) = 0.60, P(B) = 0.40, P(A∩B) = 0.24, Find (i) P(A|B) (ii) P(B|A) (iii) P(AUB) (iv) what is the relationship between A and B? 3. From a well shuffled pack of 52 playing cards, 2 cards are drawn in a succession with out replacement. Find the probability that first card is King and the second is Queen.
8. Two dice are rolled. Let X = 1 if the dice come up doubles and let X = 0 otherwise. Let Y = 1 if the sum is 4, and let y = 0 otherwise. Let Z = 1 if the dice come up both doubles and with a sum of 4 (that is, double 2), and let Z = 0 otherwise.
Suppose A and B are events with P(A) = .6, P(B) = .2, and P(B n A) = 4. Find (a) P(AU B), and (b) P(A°n B).
3. Consider the given probablity P(a)=0.7 p(b)=0.8 p(aUb)=o.8 a) Find p(aUb) b) Venn diagram c) Find p(a/b) d) find p'(a'∩ b) e) find (b/a') f) events a and b are
A of dice of sin sidad die and a pair 517-510 fatsided dlie is rollad gnd the sum is stamined.kihat isthe thobabillity that the
9(D)
2. A number U is selected at random between 0 and 1. Let the events A and B be "U differs from 1/2 by more than 1/4" and "1-U is less than 1/2", respectively. Find the events An B, Ān B, AU B.
Let A and B be two events with P(A and Bc) = 1. Find P(B). Recall that Bc denotes the complement of the event B.
5.3 A bent coin, with heads probability .2, is tossed 13 times. Let X be the number of heads in the 13 tosses. Find (a) P(X =5), and (b) P(X = 12).
1. Events A and B are mutually exclusive with P(A) = 0.280 and P(A or B) = 0.740 a) P(B)= b) P(Not A)= c) P(A and B)=
2.Direction: Classify the random variables as DISCRETE OR CONTINUOUS. 1. ev 3. 4. The 5. The speed of a car. 6. M 7. eigit of Elfel To 8. 9Percentage of the population of Kalinga. 10 Frequency of radio station. 2. ed ner houcebel Afa period Dallaing a piect. dronit in rs. touns Paris.

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1. Given two events, A and B. Find the following if P(A)=0.7, P(B)=0.5, and P(A U B)=0.9. Complete a Venn diagram before answering. (a) P(ANB) (b) P((AUB)') (c) P(A/B)