Please solve these while showing your work:

Consider the experiment of rolling a fair 6-sided die and then flipping two distinguishable fair coins (a quarter and a nickel) and recording the results as ordered triples

(x, y, z) = (number on die, result of quarter toss, result of nickel toss).

Let S be the sample space of the experiment. Moreover, define the following events:

A: The die lands on a prime number (2 or 5).

B: At least one of the coins lands on heads.

C: The number on the die is even and the two coins land on the same side

a) What is n (S)

b) Express the event A(B C)' as a set

c) Express the event A' C as a set

d) Find P (A' C). Show your work please step by step

e) Find P (C|A' ). show your work please step by step

f) Are A' and C independent events? Show your work please step by step using calculations and justify your answer