Each of a sample of four home mortgages is classified as fixed rate (F) or variable rate (). (Enter your answers in setnotation. Enter EMPTY or Ø for the empty set.)(a) What are the 16 outcomes in S?S =(b) Which outcomes are in the event that exactly three of the selected mortgages are fixed rate?(c) Which outcomes are in the event that all four mortgages are of the same type?(d) Which outcomes are in the event that at most one of the four is a variable-rate mortgage?(e) What is the union of the events in parts (c) and (d)?What is the intersection of these two events?(f) What is the union of the two events in parts (b) and (c)?What is the intersection of the two events in parts (b) and (c)?

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Answered: Each of a sample of four home mortgages…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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Let P(A) = 0.4 and P(B) = 0.5. Complete parts (a) through (d). (a) Suppose that events A and B are disjoint, find P(A or B). (b) Suppose that events A and B are independent, find P(A or B). (c) Suppose that events A and B are disjoint, find P(A | B). (d) If P(A or B) = 0.7. Are events A and B independent? (yes, no)
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.
: If you draw a card from a regular deck of 52 cards, what are the chances that your card wouldbe:(a) Red?(b) A heart?(c) A queen?(d) The queen of hearts?Your answer may be short but you must show what numbers you multiplied/divided/added/subtracted by to get your final answer. It would be written in ” P(E) = ” form.
!
R:12)
From the tree diagram find the following. (a) P(A ∩ E)(b) P(A)(c) P(A|E)
Given events A and B are independent with ?(?) = 0.7 and ?(?) = 0.4 Determine: a) P (A and B); b) P(A or B); c) P (A | B) Please include any formulas used and explanation. Thank you!
) Suppose that events A and B are independent. Show that p(A | B) + p(B)(1-p(A)) - P(A ∪ B) = 0.
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.
5. Given P(A and B) = 0.08, P(B) = 0.85, P(B|A) = 0.54, what is P(A)
(a) For each one of the statements below say whether the statement is true or false, explaining your answer. i. Let A and B be two events such that P(A) > 0 and P(B) > 0. If it holds that P(A|B) = 0, then P(B|A) = 1. 4 i. For two independent events A and B such that P(A) > 0) and P(B) > 0, then: P(AUB) = P(A) = P(B). iii. For a random variable X, then: Var(X)> Var(X + 2). iv. A random sample of size n is a sequence of n independent and non-identically distributed random variables. v. The standard normal distribution has fatter tails than the Student's t distribution with finite degrees of freedom. istribution with
Suppose P(A) = 0.7 and P(B) = 0.5. If P(A and B) = 0.3, with the help of a Venn diagram, we can estimate that P(A or B) will be a) more than 0.7 b) less than 0.5 c) more than 1.2 d) less than 0.3

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