Question

In 20 of the 36 years from 1984 through 2019, the FTSE 100 (a share index of the 100 companies listed on the London Stock Exchange with the highest market capitalization) finished higher after the first month of trading. In 18 out of those 20 years, the FTSE 100 finished higher for the year. Is a good first month a good omen for the upcoming year? The following table gives the first-month and annual performance over this 36-year period. FTSE 100’s Annual Performance First Month Higher Lower Higher 18 2 Lower 8 8 (a) If a year is selected at random, what is the probability that the FTSE 100 finished higher for the year? (Round answer to three decimal places.) (b) Given that the FTSE 100 finished higher after the first month of trading, what is the probability that it finished higher for the year? (Round answer to three decimal places.) (c) Are the two events, “first-month performance” and “annual performance,” independent? Explain.

Answer 1

P(First month higher)=20/36=5/9, P(First month lower)=4/9

P(Year High)=13/18, P(Year Lower)=5/18

P(Year high|First month higher)=18/20=9/10

c)No the two events are not independent Lets take the event-.First month high and year high

P(First month high & year high)=18/36=0.5

P(First month high)*P(Year high)=(5/9)*(13/18)=0.4012

These two should be equal in case of independence to be valid.