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(Solution Download) 1)An analyst thinks that next year there is a 70% chance that the world economy will be good, a 10%


 

 

 

 

 

 

 

1)An analyst thinks that next year there is a 70% chance that

 

the world economy will be good, a 10% chance that it will be

 

neutral, and a 20% 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.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

State of

 

the World

 

Economy

 

Probability

 

of Economic

 

State

 

Performance

 

of Creative

 

Ideas

 

Conditional

 

Probability of

 

Creative Ideas

  Good0.70

 

    Good

0.60

 

    Neutral

0.10

 

    Poor

0.30
  Neutral0.10

 

    Good

0.30

 

    Neutral

0.60

 

    Poor

0.10
  Poor0.20

 

    Good

0.50

 

    Neutral

0.40

 

    Poor

0.10

 

 

 

 

 

 

 

 

a.

 

What is the probability that the performance of the world

 

economy will be neutral and that of creative ideas will be

 

poor?

 

 

 

 

 

 

 

 

b.

 

What is the probability that the performance of Creative Ideas

 

will be poor?

 

 

 

 

 

 

 

 

c.

 

The performance of Creative Ideas was poor. What is the

 

probability that the performance of the world economy had also been

 

poor?

 

Please show all work so I am able to understand how to

 

solve.

 

 

 

 

 

3) The State Police are trying to crack down on speeding on a

 

particular portion of the Massachusetts Turnpike. To aid in this

 

pursuit, they have purchased a new radar gun that promises greater

 

consistency and reliability. Specifically, the gun advertises A????1

 

one-mile-per-hour accuracy 81% of the time; that is, there is a

 

0.81 probability that the gun will detect a speeder, if the driver

 

is actually speeding. Assume there is a 1% chance that the gun

 

erroneously detects a speeder even when the driver is below the

 

speed limit. Suppose that 78% of the drivers drive below the speed

 

limit on this stretch of the Massachusetts Turnpike.

 

 

 

 

 

 

 

 

a.

 

What is the probability that the gun

 

detects speeding and the driver was speeding?

 

 

 

 

 

 

 

 

b.

 

What is the probability that the gun

 

detects speeding and the driver was not speeding?

 

 

 

 

 

 

 

 

c.

 

Suppose the police stop a driver

 

because the gun detects speeding. What is the probability that the

 

driver was actually driving below the speed limit?

 

4) Let P(A) =

 

0.40, P(B) = 0.40, and P(A ?

 

B) = 0.18.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a.Are A and B

 

independent events?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Yes because P(A |

 

B) = P(A).

Yes because P(A ?

 

B) ? 0.

No because P(A |

 

B) ? P(A).

No because P(A ?

 

B) ? 0.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b.Are A and B

 

mutually exclusive events?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Yes because P(A |

 

B) = P(A).

Yes because P(A ?

 

B) ? 0.

No because P(A |

 

B) ? P(A).

No because P(A ?

 

B) ? 0.

 

 

 

 

 

 

 

 

 

c.What is the probability that

 

neither A nor B takes place?

 

 

 

 


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