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 up for two of the days and down for one of the days?
A)49.4%
B)43.2%
C)37.8%
D)14.4%

Question

Quizplus · Accepted Answer

The probability of the market going up two days and down one day in any order over three days can be calculated by considering all possible sequences of up (U) and down (D) days and their respective probabilities. The sequences are UUD, UDU, and DUU. 1. For UUD: The probability of UU is 0.6 * 0.7 (since there's a 60% chance it goes up on the first day and then a 70% chance it goes up again the next day). The probability of D given the previous day was U is 0.3 (since if it goes up one day, it goes down the next 30% of the time). So, the total probability for UUD is 0.6 * 0.7 * 0.3.2. For UDU: The probability of the first U is 0.6. The probability of D following a U is 0.3. The probability of U following a D is 0.8 (since if the market goes down one day, it goes up the next day 80% of the time). So, the total probability for UDU is 0.6 * 0.3 * 0.8.3. For DUU: The probability of the first D is 0.4 (since the market goes down 40% of the time). The probability of U following a D is 0.8. The probability of another U following the first U is 0.7. So, the total probability for DUU is 0.4 * 0.8 * 0.7.Adding these probabilities together gives the total probability of the market going up two days and down one day in three consecutive days:= (0.6 * 0.7 * 0.3) + (0.6 * 0.3 * 0.8) + (0.4 * 0.8 * 0.7)= 0.126 + 0.144 + 0.224= 0.494 or 49.4%.

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