Answer the following questions about the relationship between independence and mutual…
MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability
Problem
Answer the following questions about the relationship between independence and mutual exclusivity of two events A and B.
(i) Explain why two events that are mutually exclusive cannot be independent unless one of them has probability zero.
(ii) Let P(A)=0.40 and P(B)=0.35. If the events are mutually exclusive, calculate P(A∩B) and comment on whether the events can be independent.
(iii) For the same probabilities P(A)=0.40 and P(B)=0.35, if the events are instead independent, calculate P(A∩B). Discuss whether the events could still be mutually exclusive in this situation.