The prior probabilities for eventsA1, A2, and A3areP(A1) = 0.20,P(A2) = 0.30,andP(A3) = 0.50.The conditional probabilities of event B givenA1,A2,andA3areP(B | A1) = 0.50,P(B | A2) = 0.30,andP(B | A3) = 0.40.(Assume thatA1, A2, and A3are mutually exclusive events whose union is the entire sample space.)(a)ComputeP(B ∩ A1), P(B ∩ A2), and P(B ∩ A3).P(B ∩ A1)=P(B ∩ A2)=P(B ∩ A3)=(b)Apply Bayes' theorem,P(Ai | B) = P(Ai)P(B | Ai)P(A1)P(B | A1) + P(A2)P(B | A2) + + P(An)P(B | An),to compute the posterior probabilityP(A2 | B).(Round your answer to two decimal places.) (c)Use the tabular approach to applying Bayes' theorem to computeP(A1 | B),P(A2 | B),andP(A3 | B).(Round your answers to two decimal places.)EventsP(Ai)P(B | Ai)P(Ai ∩ B)P(Ai | B)A10.200.50 A20.300.30 A30.500.40 1.00 1.00

Name: The prior probabilities for eventsA1, A2, and A3areP(A1) = 0.20,P(A2)
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Description: The prior probabilities for eventsA1, A2, and A3areP(A1) = 0.20,P(A2) = 0.30,andP(A3) = 0.50.The conditional probabilities of event B givenA1,A2,andA3areP(B | A1) = 0.50,P(B | A2) = 0.30,andP(B | A3) = 0.40.(Assume thatA1, A2, and A3are mutually excl

(a)From the given information, P(A1)=0.20, P(A2)=0.30, P(A3)=0.50, P(B|A1)=0.5, P(B|A2)=0.30 and…

Answered: The prior probabilities for events A1,…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.8: Probabilities Of Disjoint And Overlapping Events

Problem 2C

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The prior probabilities for events

A₁, A₂, and A₃

are

P(A₁) = 0.20,

P(A₂) = 0.30,

and

P(A₃) = 0.50.

The conditional probabilities of event B given

A₁,

A₂,

and

A₃

are

P(B | A₁) = 0.50,

P(B | A₂) = 0.30,

and

P(B | A₃) = 0.40.

(Assume that

A₁, A₂, and A₃

are mutually exclusive events whose union is the entire sample space.)

(a)

Compute

P(B ∩ A₁), P(B ∩ A₂), and P(B ∩ A₃).

P(B ∩ A₁)

P(B ∩ A₂)

P(B ∩ A₃)

(b)

Apply Bayes' theorem,

P(A_i | B) =

P(A_i)P(B | A_i)

P(A₁)P(B | A₁) + P(A₂)P(B | A₂) + + P(A_n)P(B | A_n)

to compute the posterior probability

P(A₂ | B).

(Round your answer to two decimal places.)

(c)

Use the tabular approach to applying Bayes' theorem to compute

P(A₁ | B),

P(A₂ | B),

and

P(A₃ | B).

(Round your answers to two decimal places.)

Events	P(A_i)	P(B \| A_i)	P(A_i \| B)
A₁	0.20	0.50
A₂	0.30	0.30
A₃	0.50	0.40
	1.00		1.00

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