If events A and B are from the same sample space, and if
and , can events A and B be
mutually exclusive? Explain.
To determine if events A and B can be mutually exclusive, let's first understand what it means for events to be mutually exclusive.
Two events are said to be mutually exclusive if they cannot occur at the same time. In other words, if one event happens, the other event cannot happen. Mathematically, this can be expressed as P(A ∩ B) = 0.
In your question, we are given that events A and B are from the same sample space, denoted as Ω. This means that both events A and B are subsets of Ω, and they represent some outcomes or scenarios within the complete set of possible outcomes.
Now, if the probability of event A occurring, P(A), is 1, it means that event A is certain to happen. Similarly, if P(B) is 1, event B is certain to happen. If both events are certain to occur, it means that they cannot be mutually exclusive because they are not mutually exclusive by definition.
Therefore, when P(A) = 1 and P(B) = 1, events A and B cannot be mutually exclusive.