An event F is said to carry negative information about an event F, and we write F E, ifP(E|F) < P(E)Prove or give counterexample to the following assertions:If F E, then E F.b. If F NE and E G, then F Gа.

Answered: An event F is said to carry negative…

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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*2.100 Show that Theorem 2.6, the additive law of probability, holds for conditional probabilities. That is, if A, B, and C are events such that P(C) > 0, prove that P(A U B|C) = P(A|C) + P(B|C)–P(ANB|C). [Hint: Make use of the distributive law (AUB)NC = (ANC)U(BNC).] The Additive Law of Probability The probability of the union of two events A and B is THEOREM 2.6 P(AUB) = P(A) + P(B) – P(AN B). If A and B are mutually exclusive events, P(AN B) = 0 and P(AU B) = P(A)+ P(B).
I need answers for A, B, C Pease. There are two traffic lights on the route used by a certain individual to go from home to work. Let E denote the event that the individual must stop at the first light, and define the event F in a similar manner for the second light. Suppose that P(E) = 0.4, P(F) = 0.3, and P(E ∩ F) = 0.14. (a) What is the probability that the individual must stop at at least one light; that is, what is the probability of the event P(E ∪ F)? and What is the probability that the individual doesn't have to stop at either light? (b) What is the probability that the individual must stop at exactly one of the two lights? (c) What is the probability that the individual must stop just at the first light? (Hint: How is the probability of this event related to P(E) and P(E ∩ F)? A Venn diagram might help.)
prove that
For events X and Y, by X ⊆ Y we mean that X is a sub-event of Y. This means that if X happens, then Y must happen (and not necessarily the other way). Prove that if X ⊆ Y, then P[X] ≤ P[Y ].
Let A and B be events such that Pr[A] = 0.43, Pr[B] = 0.54, and Pr[A ∩ B] = 0.23. Find Pr[A|B] Pr[A|B] = nothing
Let S = {a, b, c, d, e, f} with P(b) = 0.13, P(c) = 0.19, P(d) = 0.3, P(e) = 0.12, and P(f) = 0.15. Let E = {a, c, d} and F = {a, c, d, e}. Find P(a), P(E), and P(F).
1. a.) What is the probability that A or B occurs? b.) What is the probability that A and B occurs? c.) What is the probability that A or B does not occur?
2.3.12 Which of the following statements are true? Explain. (a) 3a married person x such that V married people y, x is married to y. (b) V married people x, 3 a married person y such that x is married to y.
Please answer d and e. P.9.2
QUESTION 19 Statement {P(A) < P(A or B)} holds always no matter what A and B represent. O True O False
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).
Consider a manager who faces uncertainty regarding which of his employees, if any, will be the first to disturb him in his office before lunch. The state space is given by ?={Ben,Jane,Kate,Nobody}S={Ben,Jane,Kate,Nobody}. Use the proper notation to describe each of the following events (described here in words): A man is first to enter. Neither woman is the first to enter. Someone with an 'n' in their name is first to enter (to clarify, "Nobody" is not a person's name). Now suppose you are at a racetrack and about to bet on a horse race. Let ??sj denote the state in which horse j wins the race. For simplicity, suppose there are just 3 horses, and by studying the form guide, you've concluded that the probabilities of each state are given by ?(?1)=12,?(?2)=14,?(?3)=14P(s1)=12,P(s2)=14,P(s3)=14.Write down the definition for two events to be independent and explain whether or not ?1s1 and ?2s2 are independent.

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An event F is said to carry negative information about an event F, and we write F E, if P(E|F) < P(E) Prove or give counterexample to the following assertions: a. If F E, then E F.