Question

What is the correct formula for Bayes’ theorem?

Submit

Answer format: Text

unanswered

not_submitted

#16

Based on the below decision tree and the following probabilities answer the below question:

Probability of an improving economy is 0.5,

When you have an improving economy the probability of high demand is 0.7

When you have a not improving economy the probability of high demand is 0.25

What is the value of A?

Submit

Answer format: Number: Round to: 0 decimal places.

unanswered

not_submitted

#17

Our original information was that the probability of High demand was .6. We collected the following new information about what happened to demand when there was an improving or not improving economy. Answer the below question.

Calculate the probability for low demand and the improving economy (also called Joint Probability)?

Improving Economy Not improving economy

Given high demand 0.75

Given Low demand 0.54

Submit

Answer format: Number: Round to: 2 decimal places.

unanswered

not_submitted

#18

Based on the below decision tree and the following probabilities answer the below question:

Probability of an improving economy is 0.59,

When you have an improving economy the probability of high demand is 0.7

When you have a not improving economy the probability of high demand is 0.44

H

What is the value of H?

Answer 1

Baye's Theorem:

Let A₁, A₂ ,..., A_n be n mutually exclusive events forms a partition of sample space and B be any event defined on sample space then

Question no. 16:

Consider the events

A₁ : Improving economy and A₂ : Not improving economy

B: High demand

Given that

P(A₁) = 0.5 and P(A₂) = 0.5

P(B/A₁) = 0.7 and P(B/A₂) = 0.25

A = P ( High demand) = P (A₁) * P(B/A₁) + P(A₂) * P(B/A₂)

= 0.5 *0.7 + 0.5 +0.25

A= 0.475

Question no .17 :

Consider

A₁: High demand and A₂: Low demand

B : Improving economy

P(A₁) = 0.6 , P(A₂) = 0.4 and P(B / A₂) = 0.54

Required probability = P ( Low demand and improving economy) =

= P(A₂) * P(B / A₂)

= 0.4 * 0.54 = 0.216

Question no. 18:

Consider

A₁: improving economy and A₂: Not improving economy

B : High demand

P(A₁) = 0.59 and P( A₂) = 0.41

P(B/A₁) = 0.7 and P(B/A₂) = 0.44

H=P ( High demand) = P(A₁) * P(B/A₁) + P(A₂) + P(B/A₂)

= 0.59 * 0.7 + 0.41 *0.44

= 0.5934