SOLUTION: A red dye and a green die are rolled as a pair. Let E be the event that "the red die shows a 2" and let F be the event that "the sum of the numbers is 8." Are the events E and F in

The probability of event E  is  P(E) = .



The probability of event F  is  P(F) =  

    (since there are 5 pairs with the sum 8  (2,6), (3,5), (4,4), (5,3), (6,2)  among 36 possible outcomes - pairs (m,n), 

    where m and n are integers between 1 and 6 inclusively).



The probability of event  (E & F)  is  P(E & F) = 

    (since there is only one pair (red2, green6) with the sum 8 among 36 possible outcomes - pairs (m,n), 

    where m and n are integers between 1 and 6 inclusively).



Now,  the product  P(E)*P(F)  is equal to   = ,   while  P(E & F) = .



As you see,   P(E)*P(F)  is not equal to  P(E & F),  therefore events E and F are not independent.     ANSWER