A string of 10 ternary digits 012 is formed Let E be the eve

A string of 10 ternary digits (0,1,2) is formed. Let E be the event that the first digit is 0, F be the event that the last digit is 0, and G be the event that the first digit is the same as the last.

a) Find n(E), n(F), and n(G)

b) Find n(E intersect F)

c) Find n(E union F)

d) Find n((E union)F) intersect G)

Please show all work and explain your methods.

Solution

a) n(E) = first digit 0 and remaining 9 any of the 3

            = 1*3^9 = 3⁹

b) n(E int F) = First and last 0 remaining any of the 3

                    = 3⁸

c) n(EUF) = 3⁹ (since F is a subset of E)

d) n(EUF int G) = n(F) = 3⁸