given: two unbiased dice are thrown

formula:

total possible outcomes of from the dice is ⁶C₁⁶C₁

therefore n(S)=36

(i) let E be the event that neither a doublet nor a total of 8 will appear

E’ be the event that a doublet or a total of 8 occurs

E’= {(1,1) (2,2) (3,3) (4,4) (5,5) (6,6) (2,6) (6,2) (3,5) (5,3)}

n(E’) = 10

Therefore P(E) is

(ii) let E be the event that sum of number obtain on the dice is neither a multiple of 2 or 3

E’ be the event that sum of number obtain on the dice is either a multiple of 2 or 3, that is total should be 2,3,4,6,8,9,10,12

E’= {(1,1) (1,2) (2,1) (1,3) (2,2) (3,1) (1,5) (2,4) (3,3) (4,2) (5,1) (2,6) (3,5) (4,4) (5,3) (6,2) (3,6) (4,5) (5,4) (6,3) (4,6) (5,5) (6,4) (6,6)}

n(E’) = 24

Therefore P(E) is