(a) Define the terms “mutually exclusive events” and “independent events” for a…
MATHEMATICS · Subjective · A Level · Mathematics · Probability · Probability
Problem
(a) Define the terms “mutually exclusive events” and “independent events” for a random experiment.
(b) Explain, in your own words, the fundamental logical difference between these two kinds of events.
(c) Is it possible for two events, each having positive probability, to be both mutually exclusive and independent at the same time? Give a clear reason for your answer.
(d) Construct one illustrative example (specify the experiment, sample space, and the two events) where the two events are independent but not mutually exclusive. Verify all required probabilities to justify your claim.