In 46 of the 70 years from 1934 through 2003 a certain stock

In 46 of the 70 years from 1934 through 2003 a certain stock market finished higher after the first week of trading. In 38 of those 46 years, this market finished higher for the year. The following table gives the first-week and annual performance of the market over this 70-year period. Use the table to answer (a) through (c) below. It a year is selected at random, what is the probability that the market finished higher for the year? (Round to from decimal places as needed.) Given that the market finished higher after the first week of trading, what is the probability that it finished higher for the year? (Round to four decimal places as needed.) Are the two events \"first-week performance\" and \"annual performance\" independent?\' Explain. Yes, the probabilities in (a) and (b) are not equal which means that neither even: affects the probability of occurence of the other event. Yes, the probabilities in (a) and (b) are equal which means that neither event affects the probability of occurence of die other event No, the probabilities in (a) and (b) are equal, which means that one event affects the probability of occurence of the other event. No, the probabilities in (a) and (b) are not equal, which means that one event affects the probability of occurence of the other event.

Solution

a. P(Higher for year) = (38+12) / (38+12+ 8+12) = 0.7143

b. P(Higher for year | Higher for first week) = (38)/ (38+12) = 0.76

c. No, the probailities in a and b are not equal, so they are not independent.

Answer: 4th Option