Consider the following statements:i. If A and B are independent, then Ā and B must be independent.ii. The sum of the probabilities of collectively exhaustive events must equal one.iii. If A and B are mutually exclusive, then Ā and B must be mutually exclusive.iv. P(AUB) = P(A) + P(B)[1-P(A|B)]Which of the following is correct about the statements?a. (ii) and (iii) are true.b. None of the suggested answers are correct.O c. (i) and (iv) are true.O d. (i) and (ii) are true.е.All are false.

Answered: Image /qna-images/answer/58df8153-61eb-433b-9d8e-9ef126236681.jpg

Answered: Consider the following statements: i.…

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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of 16 Suppose a high school gymnasium bag contains volleyballs, basketballs, and soccer balls. During physical education class, the coach randomly selects a ball 0.45 0.37 from the bag. The ball the coach selects determines what sport the students play that day. If she selects a volleyball, the students play volleyball that day, and so 0.45 0.18 on. The tree diagram shows the possible outcomes with their probabilities for two consecutive physical education classes. Determine the probability that the students will play volleyball two days in a row. Give your answer as a decimal precise to two decimal places. 0.45 0.37 0.37 0.18 0.18 0.45 0.37 0,18
Let P(E) = 0.45, P(F) = 0.4, and P(F ∩ E) = 0.25. Draw a Venn diagram and find the conditional probabilities. (a) P(E | FC )(b) P(F | EC )
There are 35 students are in the classroom 20 girls and 15 boys two students selected randomly find the given probabilities 1- first is boy and secound is girl 2 both are boys 3- both are girls
Example 3-28. Let P (A) = p, P (A \B) = q, P (B | A) = r. Find relations betwe number p, q, r for the following cases : (a) Events A and B are mutually exclusive. (b) A and B are mutually exclusive and collectively exhaustive. (c) A is sub-event of B ; B is a sub-event of A. (d) Ā andB are mutually exclusive.
*21. A and B are events such that P(A) = 0.4, P(B)=0.5, and P(A & B) = 0.2. Answer each question and explain your reasoning. a. Are A and B mutually exclusive? b. Are A and B independent?
Che
7. A drawer contains 6 black socks, 4 brown socks, and 2 green socks. Suppose one sock is drawn from the drawer and that it is equally likely that any one of the socks is drawn. Find the probabilities for each of the following: a. The sock is brown b. The sock is either black or green c. The sock is red d. The sock is not black
Which one of the following statements is False (not true)? Events A and B are independent if and only if P(A and B) = P(A) x P(B). Events A and B are independent if and only if P(A) = P(A given B). O(A) x O(not A) = 1 Events A and B are independent if and only if A and B are mutually exclusive; that is disjoint. If events A and B are mutually exclusive then, P (A or B) = P(A) + P(B).
Let P(E) = 0.4, P(F) = 0.3, and P(F ∩ E) = 0.2. Draw a Venn diagram and find the conditional probabilities. (a) P(E | FC )(b) P(F | EC )
Which of the following values cannot be probabilities? 1, 1.49, 0.09, 3/5, 0, 5/3, - 0.45, /2 Select all the values that cannot be probabilities. O A. 1.49 O B. 0.09 O C. 5 3 O D. 1 O E. - 0.45 OF. V2 O G. 3 O H. 0
Prove the theorem
4. 60% of homeowners in Northern Virginia have a weekly lawn service. Those homes with a lawn service, 55% have a sprinkler system. For those without a lawn service, 30% have a sprinkler system. (Note: you do NOT need to simplify these answers. However, you MUST express each in terms of the events/probability notation – e.g., P(A|B) =..) a. Draw a tree diagram to model the problem b. What is the probability that a randomly selected home has a sprinkler system? c. What is the probability that a randomly selected home with a sprinkler system has a lawn service? d. What is the probability that a randomly selected home with a lawn service has a sprinkler system? e. What is the probability that a randomly selected home has a lawn service? f. What is the probability that a randomly selected home that does not have a lawn service has a sprinkler system?

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