MATHEMATICS · Multi-part · A Level · Mathematics · Probability · Probability
Problem
A fair coin is tossed twice. Consider the following events defined on the sample space:
A: “the first toss shows Heads”
B: “at least one Head occurs in the two tosses”
C: “both tosses show the same result.”
(i) List the sample points belonging to each of the events A, B and C.
(ii) Determine the probabilities P(A), P(B) and P(C).
(iii) For each pair (A, B), (A, C) and (B, C), compute P(pair) and test whether the events in the pair are independent.
(iv) For each pair above, state whether the events are mutually exclusive and justify your answer.
(v) Summarise your findings to highlight the conceptual difference between independence and mutual exclusivity in this experiment.