A coin is tossed three times. Consider the following events
A: Heads on the first toss.
B: Tails on the second.
C: Heads on the third toss.
D: All three outcomes the same (HHH or TTT).
E: Exactly one head turns up.
(a) Which of the following pairs of these events are independent? i. A, B ii. A, D iii. A, E iv. D, E
(b) Which of the following triples of these events are independent? i. A, B, C ii. A, B, D iii. C, D, E
Consider a fair coin flipped a number of times.
(a) Which event is more likely HHHHHHHHH or HHHHHHHHT?
(b) Calculate the probability of each event.
(c) If someone thinks the first event is more likely, they are suffering from what?
(d) If someone thinks the second even is more likely, they are suffering from what?