Question

An analyst thinks that next year there is a 70% chance that the world economy will be good, a 20% chance that it will be neutral, and a 10% chance that it will be poor. She also predicts probabilities that the performance of a start-up firm, Creative Ideas, will be good, neutral, or poor for each of the economic states of the world economy. The following table presents probabilities for three states of the world economy and the corresponding conditional probabilities for Creative Ideas.

a. What is the probability that the performance of the world economy will be neutral and that creative ideas will be poor? (Round your answer to 2 decimal places.)

b. What is the probability that the performance of Creative Ideas will be poor? (Round your answer to 2 decimal places.)

c. The performance of Creative Ideas was poor. What is the probability that the performance of the world economy had also been poor? (Round your answer to 2 decimal places.)

23 An analyst thinks that next year there is a 70% chance that the world economy will be good, a 20% chance that it will be neutral, and a 10% chance that it will be poor. She also predicts probabilities that the performance of a start-up firm, Creative Ideas, will be good, neutral, or poor for each of the economic states of the world economy. The following table presents probabilities for three states of the world economy and the corresponding conditional probabilities for Creative Ideas. 0.92 points State of the World Economy Good Probability of Economic State 0.70 eBook Conditional Probability of Creative Ideas 0.20 0.30 0.50 0.70 0.20 0.10 0.30 Neutral Performance of Creative Ideas Good Neutral Poor Good Neutral Poor Good Neutral Poor 0.20 Hint Poor 0.10 Print Click here for the Excel Data File References a. What is the probability that the performance of the world economy will be neutral and that of creative ideas will be poor? (Round your answer to 2 decimal places.) Probability 0.03 b. What is the probability that the performance of Creative Ideas will be poor? (Round your answer to 2 decimal places.) Probability 0.30 c. The performance of Creative Ideas was poor. What is the probability that the performance of the world economy had also been poor? (Round your answer to 2 decimal places.) Probability F < Prev 23 of 27 Next > Type here to search о н о е ё а я

Answer 1

a )

Probability that the performance of the world economy will be neutral and that of creative ideas will be poor is,

= 0.2*0.1 = 0.02

b)

Probability that the performance of Creative ideas will be poor is ,

= 0.7*0.5+ 0.2*0.1 + 0.1*0.3 = 0.4

c)

P( Economy had poor | Creative idea was poor )

= P( Economy had poor and Creative idea was poor ) / P( Creative idea was poor )

{ Using conditional probability formula ,    P( A | B ) = P( A and B ) / P( B ) }

P( Economy had poor and Creative idea was poor ) = 0.1*0.3 = 0.03

P( Creative idea was poor ) = = 0.7*0.5+ 0.2*0.1 + 0.1*0.3 = 0.4

So,

P( Economy had poor | Creative idea was poor )   = 0.03/ 0.4 = 0.075