## (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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