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Consider an experiment of drawing two cards at random from a bag containing four cards marked with the integers 1 through 4. (a) Find the sample space S, of the experiment if the first card is replaced before the second is drawn. (b) Find the sample space S, of the experiment if the first card is not replaced. Q7:- Using a Venn diagram, Prove the following:- An (Bu C) = (A n B) U (An C)

Consider an experiment of drawing two cards at random from a bag containing four cards marked with the integers 1 through 4. (a) Find the sample space S, of the experiment if the first card is replaced before the second is drawn. (b) Find the sample space S, of the experiment if the first card is not replaced. Q7:- Using a Venn diagram, Prove the following:- An (Bu C) = (A n B) U (An C)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Q6 Consider an experiment of drawing two cards at random from a bag containing four cards marked with the integers 1 through 4. (a) Find the sample space S, of the experiment if the first card is replaced before the second is drawn. (b) Find the sample space S, of the experiment if the first card is not replaced. Q7:- Using a Venn diagram , Prove the following:- A o (B u C) = (A o B) U (A n C) Q8 Let P(A) = 0.9 and P(B) = 0.8. Show that P(A B) 2 0.7. Q9 Given that P(A) = 0.9, P(B) = 0.8, and P(A n B) = 0.75, find (a) P(A u B); (b) P(A n B); and (c) P(Ān B). Q10 Consider a telegraph source generating two symbols, dots and dashes. We observed that the dots were twice as likely to occur as the dashes. Find the probabilities of the dot's occurring and the đash's occurring. Q11 The sample space S of a random experiment is given by S= {a, b, c, d} with probabilities P(a) = 0.2, P(b) = 0.3, P(c) = 0.4, and P(d) = 0.I. Let A denote the event {a, b), and B the event {b, c, d}. Determine the following probabilities: (a) P(A); (b) P(B); (c) P(Ã); (d) P(A U B); and (e) P(An B). Q12 A committee of 5 persons is to be selected randomly from a group of 5 men and 10 women. (a) Find the probability that the committee consists of 2 men and 3 women, (b) Find the probability that the committee consists of all women.
Transcribed Image Text:Q6 Consider an experiment of drawing two cards at random from a bag containing four cards marked with the integers 1 through 4. (a) Find the sample space S, of the experiment if the first card is replaced before the second is drawn. (b) Find the sample space S, of the experiment if the first card is not replaced. Q7:- Using a Venn diagram , Prove the following:- A o (B u C) = (A o B) U (A n C) Q8 Let P(A) = 0.9 and P(B) = 0.8. Show that P(A B) 2 0.7. Q9 Given that P(A) = 0.9, P(B) = 0.8, and P(A n B) = 0.75, find (a) P(A u B); (b) P(A n B); and (c) P(Ān B). Q10 Consider a telegraph source generating two symbols, dots and dashes. We observed that the dots were twice as likely to occur as the dashes. Find the probabilities of the dot's occurring and the đash's occurring. Q11 The sample space S of a random experiment is given by S= {a, b, c, d} with probabilities P(a) = 0.2, P(b) = 0.3, P(c) = 0.4, and P(d) = 0.I. Let A denote the event {a, b), and B the event {b, c, d}. Determine the following probabilities: (a) P(A); (b) P(B); (c) P(Ã); (d) P(A U B); and (e) P(An B). Q12 A committee of 5 persons is to be selected randomly from a group of 5 men and 10 women. (a) Find the probability that the committee consists of 2 men and 3 women, (b) Find the probability that the committee consists of all women.
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