Select all the statements or equations that show that events A and B are independent.P(A and B) = P(A) · P(B)O P(A or B) = P(A) + P(B) – P(A and B)P(A | B) = P(A) and P(B| A) = P(B)%3DP(A) is the same whether event B happens or not.P(A and B)P(A|B)P(A)

first condition P(A and B) = P(B)*P(B) this is show the independent events second statement show…

Answered: Select all the statements or equations…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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) Suppose that events A and B are independent. Show that p(A | B) + p(B)(1-p(A)) - P(A ∪ B) = 0.
Determine whether the events A and B are independent. P(Ac) = 0.3, P(Bc) = 0.1, P(A ∩ B) = 0.63 Yes or No
The intersection of two events occurs when A Event A and event B are independent Event A and event B are mutually exclusive Both event A and event B occur Either event A or event B occur
P(A) + P(B) = 1 for any events A and B that are mutually exclusive. True False
Events A and B are such that P(A)=0.30 and P(A or B)=0.60. Given that A and B are independent and non-mutually exclusive, determine P(B).
Let A and B be two events with P(A and Bc) = 1. Find P(B). Recall that Bc denotes the complement of the event B.
For each set of probabilities, determine whether the events A and B are independent or dependent. (If necessary, consult a list of formulas.) Probabilities Independent Dependent = P(A 18) - 1 (a) P(A)=-;P(B) =;P(A\B) = 5 1 1 P(A) =;P (B) = P(A and B) = %3D 4 6. 1 1 P (B|A) = 1 (c) P(4)-극: P(B)-P(Bl4): %3D %3D 1 1 (d) P(A) = : P(B) = P(4 |B) = | %3D
Determine if the events E and F are independent. P(E) = 0.76, P(F) = 0.7, P(En F) = 0.51 O independent O not independent O cannot be determined
(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
Event E and event F are independent. Fiven P(E) = 0.3, P = (F) 0.5, compute P(E and F) and P(E or F). a) P(E and F) = b ) P(E or F)
Let A and B be events with P (A) = 0.5, P(B) = 0.95, and P (B|A) = 0.1. Find P (A and B). P(A and B) -0

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Select all the statements or equations that show that events A and B are independent. O P(A and B) = P(A) · P(B) O P(A or B) = P(A) + P(B) – P(A and B) O P(A|B) = P(A) and P(B| A) = P(B) O P(A) is the same whether event B happens or not. P(A|B) = P(A and B) %3D P(A)