MATHEMATICS · Multi-part · A Level · Mathematics · Probability · Probability
Problem
Let A be any event in a sample space S.
(i) Prove that P(A′)=1−P(A) by treating A and its complement A′ as suitable events and using only the three axioms of probability.
(ii) A fair coin is tossed five times. Without listing all possible outcomes, use the result of part (i) to find the probability of getting at least one head.
(iii) Treat the events “exactly k heads” for k=1 to 5 as mutually exclusive. Using the additivity axiom, verify that the sum of their probabilities equals the answer obtained in part (ii).