Question

An economist believes that during periods of high economic growth, the U.S. dollar appreciates with probability 0.70; in periods of moderate economic growth, the dollar appreciates with probability 0.40; and during periods of low economic growth, the dollar appreciates with probability 0.20. During any period of time, the probability of high economic growth is 0.30, the probability of moderate economic growth is 0.50, and the probability of low economic growth is 0.20. Suppose the dollar has been appreciating during the present period. What is the probability we are experiencing a period of high economic growth?

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Answer 1

solution:

From the given datd is

High economic growth = H

Moderate economic growth = M

Low economic growth = L

Any period of time = A

Now,

we need to assigning the probabilities,

P(H) = 0.70

P(M) = 0.40

P( L) = 0.20

P(A/ H) =0.30

P(A / M) = 0.50

P (A / L ) = 0.20

P( A) is a probability of appreciating

P(A0 = P(A/M) P(H)+P(A/M) P (M)+P(A/L)P(L)

(0.30x 0.70)+(0.50x0.40) +(0.20x 0.20)

= 0.45

the dollar has appreciating during the present period

In the probability we are experience a period of high economic growth.

P(HnA) P(A) P(A|H) P(H) P(A) P(H|A) P(AIH)P(H) P(AH)P(H)+ P(A| M)P (M) +P(A|L)P(L) (0.30x0.70) (0.30x0.70)+(0.50x0.40)+(0.20x0.20) = 0.4667

$\therefore$ High economic growth P(H/A) = 0.4667

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Answer 2

Add you answer here...P(H/A)is 0.4667,P(M/A) is 0.4444 and P(L/A) is 0.0880