Events A₁ and A2 are mutually exclusive and form a completepartition of a sample space S with P(A₁) =0.48. If E is anevent in S with P (E| A₁) =0.25 and P(E|A₂) = 0.09,compute P(A₁ | E) =? (Hint: Because A₁ and A2 are mutuallyexclusive and form a complete partition of the sample space,P(A₂) = 1-P (A₁)).Note: If your final answer has up to four decimal places, please enter yourfull answer without rounding it. If your answer contains more than fourdecimal places, please round it to four decimal places before entering it inthe box below.

Given that A1 and A2 are mutually exclusive events.P(A1)=0.48P(A2)= 1-P (A1) = 1-0.48 = 0.52P(E|A1)…

Answered: Events A₁ and A2 are mutually exclusive…

A First Course in Probability (10th Edition)

10th Edition

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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 A and B be events in a sample space S such that S = A ∪ B. Suppose that P(A) = 0.4, P(B) = 0.8, and P(A ∩ B) = 0.2. Find each of the following. (a) P(A ∪ B) (b) P(Ac ∪ Bc )
(i) Show that if P(A) = 0 or P(A) = 1, then A is independent of every other event. Show that if A is independent of itself then P(A) is either O or 1. (ii) Suppose k events form a partition of the sample space N, i.e., they are disjoint and UL, A; = N. Assume that P(B) > 0. Prove that if P(A1|B) P(A;) for some i = 2, ..., k.
Let A and B be two events in a sample space S such that P(A) = 0.5, P(B) = 0.5, and P(A ∩ B) = 0.24. Find the probabilities below. (a) P(A|B)(b) P(B|A)
In a sample space S, the two events A,B are such that P(A) = .6, P(B) = .2, P((AN B)c) = .9. What is P(An B)? Ο ΡΑB) 6 O P(AN B) = .1 (answer) O P(AN B) = .12 Ο Ρ(An B ) -0 In a sample space S, the two events A,B are such that P(A) = .6, P(B) = .2, P((An B)°) = .9. The events A and B are: O Mutually Exclusive O Independent O Neither Mutually Exclusive nor Independent (answer) O Both Mutually Exclusive and Independent
For any two events A, B, and sample space S, state True or false: • If P(A) + P(B) = P(AU B) then P(AN B) = 0. • If P(AN B) = 0 then P(AU B) = P(A) + P(B). • The sample space, S, is always independent of any event A.
A sample space consists of just three outcomes, denoted 0,, 02, and O. Events E. F. and G are defined as E={O1,02} F = {O2,O3 } G = {O1, O3} If Pr[E] = 0.77 and Pr[F] = 0.52, what is Pr[G]? (A) 0.645 (В) 0.77 (C) 0.355 (D) 0.29 (E) 0.23 (F) 0.48 (G) 0.52 (Н) 0.71 O A OB O D O E
Events A₁ and A2 are mutually exclusive and form a complete partition of a sample space S with P (A₂) = 0.39. If E is an event in S with P (E | A₁) =0.12 and P(E|A₂) = 0.18, compute P(A₂2 | E) =? (Hint: Because A₁ and A2 are mutually exclusive and form a complete partition of the sample space, P(A₁) = 1 − P (A₂) ). = Note: If your final answer has up to four decimal places, please enter your full answer without rounding it. If your answer contains more than four decimal places, please round it to four decimal places before entering it in the box below.
A sample space consists of just three outcomes, denoted O1, O2, and O3. Events E, F, and G are defined as E = {O1,O2 } F = {O2,O3 } G = {O1,03 } If Pr[E] = 0.77 and Pr[F] = 0.52, what is Pr[G]? %3| %3D (A) 0.645 (B) 0.77 (C) 0.355 (D) 0.29 (E) 0.23 (F) 0.48 (G) 0.52 (H) 0.71
Let A and B be events in a sample space S such that P(A) = 21/100, P(B) = 2/5, and P(AB) = 13/100. Find P( B | Ac ). A) 0.3148 B) 0.5250 C) 0.5063 D) 0.1646 E) 0.6750
Events A1 and A2 are mutually exclusive and form a complete partition of a sample space S with P(A1) = 0.39, and P(A2) = 0.61. If event E is an event in S with P (E I A1) = 0.08 and P(E I A2) = 0.10, using Bayes' theorem compute P(A1 I E) = ? (Round final answer to four decimal places and select best option below).0.5602 0.6113 0.1004 0.4671 0.3384 0.2698 Correct answer is not listed 0.0992

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