An economist believes that during periods of high economic growth in the United States, 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 growth is 0.50, and the probability of low economic growth is 0.20.

a. Assuming the U.S. dollar has been appreciating during the present period, and assuming that the economist is correct, determine the probabilities that the U.S. is experiencing a period of high, moderate, and low economic growth.

b. Assuming the U.S. dollar has been depreciating during the present period, and assuming that the economist is correct, determine the probabilities that the U.S. is experiencing a period of high, moderate, and low economic growth.