(a) Define independent events in the context of probability.
An experiment consists of tossing two fair coins simultaneously. Let
A = "the first coin shows Heads" and
B = "the second coin shows Tails".
Let
C = "at least one of the two coins shows Heads" and
D = "both the coins show Tails".
(b) Show, with calculation, whether A and B are independent.
(c) Determine, with reasons and calculation, whether the pair of events C and D are independent.
a. (i) Define independent events.
b. (ii) Show whether A and B are independent.
c. (iii) Determine whether C and D are independent and justify your answer.