In 48 of the 80 years from 1926 through 2005 a certain stock market finished hig
ID: 3271470 • Letter: I
Question
In 48 of the 80 years from 1926 through 2005 a certain stock market finished higher after the first week of trading. In 45 of those 48 years, this market finished higher for the year. The following table gives the first-week and annual performance of the market over this 80-year
period. Use the table to answer (a) through (c) below.
ANNUAL PERFORMANCE
FIRST WEEK
Higher
Lower
Higher
45
3
Lower
16
16
a. If a year is selected at random, what is the probability that the market finished higher for the year?
(Round to four decimal places as needed.)
b. 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.)
c. MULTIPLE CHOICE: Are the two events "first-week performance" and "annual performance" independent? Choose one
A. No, the probabilities in (a) and (b) are equal, which means that one event affects the probability of occurence of the other event.
B. No, the probabilities in (a) and (b) are not equal, which means that one event affects the probability of occurence of the other event.
C. Yes, the probabilities in (a) and (b) are equal, which means that neither event affects the probability of occurence of the other event.
D. Yes, the probabilities in (a) and (b) are not equal, which means that neither event affects the probability of occurence of the other event.
ANNUAL PERFORMANCE
FIRST WEEK
Higher
Lower
Higher
45
3
Lower
16
16
Explanation / Answer
Ans:
a)P(higher annual performance)=0.7625
b)P(higher annual performance/higher first week performance)
=P(higher annual and higher first week performance)/P(higher first week performance)
=0.5625/0.6
=0.9375
c)P(higher annual performace and higher first week performance)=0.5625
P(higher annual performance)*P(higher first week performance)=0.7625*0.6=0.4575
Both are not equal,hence both events not independent.
or
the probabilities in a) and b) are not equal,which means that one event affects the probability of occurence of the other event.
hence,both events are not independent.
Option B is correct.
Annual performance Total First week Higher Lower Higher 45 3 48 Lower 16 16 32 Total 61 19 80