In Discrete Mathematics!!!!!!!!!! III.Find the following:i)ii)iii)iv)V)vi)Sets1. Let U= the set of all nonnegative real numbers less than 10.A= {x € U: x is counting number}B= {x € U: 0 less than equal to x but x is less than 5}C= {0,1,5}Set A using roster methodSet U in interval formn(A)ANBOCC\AB'

Let U = the set of all non negative real numbers less than 10 i.e., U = [0,10) (Note that, as the…

Answered: III. Find the following: i) ii) iii) v)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Problem 1. Suppose you roll a fair 20-sided die. Are the following events independent? (a) E₁ is the event that the result of the die roll is even. E2 is the event that the result of the die roll is less than or equal to 6. (b) E₁ is the event that the result of the die roll is even. E2 is the event that the result of the die roll is divisible by 4. (c) E₁ is the event that the result of the die roll is divisible by 4. E₂ is the event that the result of the die roll is divisible by 6. (d) E₁ is the event that the result of the die roll is divisible by 4. E2 is the event that the result of the die roll is divisible by 5.
6. Establish what is meant by (a) a pair of mutually exclusive events and (b) a pair of statistically independent events. Prove, with reference to the axioms of probability and the rules of boolean algebra, that P(AUB) = P(A) + P(B) – P(AN B). The probability that a smoker who consumes over 40 cigarettes a day will suffer from chronic respiratory illness is 0.4. The probability that he will suffer from heart disease is 0.5. The probability that he will suffer from at least one of these ailments is 0.6 (i) Find the probability that the smoker will suffer from both ailments, (ii) Find the probability that he will suffer from heart disease given that he suffers from chronic respiratory illness.
Rework problem 16 from the Chapter 2 review exercises in your text, involving the sum of two die rolls. (1) What is the probability they sum to 2, 5, or 10? (2) What is the probability they sum to at least 11?
An experiment consists of tossing a coin twelve times and observing the sequence of heads and tails. (a) How many different outcomes are possible? (Simplify your answer.) (b) How many different outcomes have exactly six heads? (Simplify your answer.)
If you flip 10 fair coins, what is the probability that: (a) Exactly 5 of them are “heads”? (b) At least 8 of them are “heads”? Can you explain the formula step by step ?
1. Suppose you roll three fair dice number on the red die, lies strictly between the other two numbers? For this problem, your solution should be short and intuitive, with a final answer that is a single number (e.g., a fraction) rather than anything in summation form or similar. one red, one blue, and one green. What's the probability that the
The Ramos family combined annual income is 850,000 pesos last year, This Year, the said amount increased by an additional 150,000 pesos. Find the ratio of Ramos Family's combined annual income for this year compared last year.
Probability questions can be tricky because they are sensitive to the precise kind of information (i.e. conditioning) available. This problem is taken from Machine Learning: a Probabilistic Perspective by Kevin Murphy. My new neighbors have two children. Let’s assume the sexes of their children are independent from one another, each with probability 1 2 , so that all four possibilities {(B, B),(B, G),(G, B),(G, G)} are equally likely (we are writing the sexes in (oldest, youngest) order). (a) If I ask my neighbors whether they have any boys, and they say “yes,” then what is the probability that one of their two children is a girl? Clearly list out the sample space and associated probabilities. (b) Suppose instead that I happen to see one of their children run by, and it’s a boy. What is the probability that their other child is a girl? (Hint: what is this probability if the child I saw was their oldest child? How about their youngest? How can we synthesize this information to get an…
Subject: Statistics & Probability Formula: The probability of an event A can be computed using the following formula No.of Desired Outcomes P(A) || No. of Possible Outcomes Questions: A. Calculate for the probability of the following. 1. A fair coin is tossed 3 times, what is the probability of getting: a. 2 heads and 1 tail b. Exactly 3 heads c. At least 1 head 2. Getting an odd number and a tail when a single die is rolled, and a coin is tossed at the same time? 3. From the number 1 15, what is the probability of getting: a. Numbers greater than 7 b. Numbers less than 10 c. Numbers between 3 and 13

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III. Find the following: i) ii) iii) v) vi) Sets 1. Let U= the set of all nonnegative real numbers less than 10. A= {x € U: x is counting number} B= {x € U: 0 less than equal to x but x is less than 5} C= {0,1,5} Set A using roster method Set U in interval form n(A) ANBOC CA B'