MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability
Problem
Three events A, B and C can occur on any given day in a weather–monitoring experiment. Exactly one of these events occurs on each day, so they are mutually exclusive and exhaustive. The probabilities are in the ratio P(A):P(B):P(C)=2:3:5.
Answer the following questions.
(i) Determine P(A), P(B) and P(C).
(ii) Let E be the event that either A or B occurs. Find P(E).
(iii) Are the events E and C mutually exclusive? Are they exhaustive together? Give reasons based on your answers above.
(iv) A second experiment is conducted on another day. Assuming independence between the two days, compute the probability that event C occurs on both days.