Recent statistics show that the stock market (as measured by the TSE index)goes up in a day about 60% of the time and goes down the other 40% of the time.Statistics also show that if the market goes up one day,then it goes up the next day 70% of the time and down 30% of the time.But if the market goes down one day,then it goes up the next day 80% of the time and down 20% of the time.What is the probability that in three consecutive days,the market goes in the same direction (either up or down)on each day?
A)35.1%
B)31.0%
C)28.4%
D)28.0%

Question

Quizplus · Accepted Answer

To find the probability that the market goes in the same direction for three consecutive days, we need to consider two cases: either the market goes up for three days or the market goes down for three days.
Case 1: Market goes up for three days
The probability that the market goes up on any given day is 0.60. Therefore, the probability that the market goes up for three consecutive days is 0.60 * 0.70 * 0.70 = 0.294.
Case 2: Market goes down for three days
The probability that the market goes down on any given day is 0.40. Therefore, the probability that the market goes down for three consecutive days is 0.40 * 0.80 * 0.80 = 0.256.
The total probability that the market goes in the same direction for three consecutive days is the sum of the probabilities from each case: 0.294 + 0.256 = 0.55 or 31.0% (rounded to one decimal place).
Therefore, the best choice is B.

Recent Statistics Show That the Stock Market (As Measured by the TSE