I need very detailed answers. the goal of these exercises are for me to understand the entire process in anticipation of my exam. Please include any information necessary in solving the problems

91705 assignment
2.
Let A1 be the event that either all 3 are heads or all three are tails
Sample space = (HHH, HHT, HTH, HTT, THH, THT, TTH, TTT)
A2, exactly 2 heads and A3 exactly 1 head
A1 = (HHH, TTT) : P(A1) = 2/8
A2 = (HHT, HTH, THH): P(A2) = 3/8
A3 (HTT, THT, TTH ):P(A3) = 3/8
We find if first two are heads third getting head or tail is independent.
But two heads one tail or three heads are not mutually independent.
Prob...