Events are exhaustive if all possible outcomes have been included.
For a single event, they are exhaustive only if all possible outcomes have been considered.
When all the probabilities for one event are added together, they must add up to 1. This is shown as (for an outcome of A:
P(A) + P(not A) = 1
A dice is thrown. Is rolling an even number and rolling a prime number exhaustive?
P(even) covers 2, 4, 6
P(prime) covers 2, 3, 5
1 is not included, and therefore the statement is not exhaustive.
A bias dice is thrown. Explain why does this not change the exhaustive events.
Answer: Exhaustive events must cover all possible outcomes: it does not specify the values or fairness of the outcomes.