Let’s define two events a and B in the same sample space. Their probabilities are as follows:
P(A) = 0.5
P(B) = 0.6
Is it possible for events A and B to be disjoint?
No, it is not possible for events A and B to be disjoint if their probabilities are both greater than zero. Disjoint events, also known as mutually exclusive events, are events that cannot occur at the same time. In other words, if events A and B are disjoint, then the probability of both events occurring together is zero (P(A ∩ B) = 0). However, since both P(A) and P(B) are greater than zero, it means that there is a non-zero probability of A and B occurring together, which means they are not disjoint.
Yes, it is possible for events A and B to be disjoint. Two events are considered disjoint or mutually exclusive if they cannot occur at the same time, meaning that if one event occurs, the other event cannot occur. In this case, the probabilities of events A and B are independent of each other. Therefore, if P(A) = 0.5 and P(B) = 0.6, it is possible for events A and B to be disjoint as long as the intersection of A and B, denoted as A ∩ B, has a probability of 0.
To determine if events A and B can be disjoint, we need to check if they have any common outcomes.
Two events are called disjoint if they have no outcomes in common. In other words, if event A occurs, then event B cannot occur, and vice versa.
In this case, if event A and event B are disjoint, it means they cannot happen at the same time. However, if the probabilities of A and B are both greater than zero, it is not possible for them to be disjoint.
Here's how to check if events A and B are disjoint:
1. Look at their probabilities: P(A) = 0.5 and P(B) = 0.6.
2. If both probabilities are greater than zero, it means that there are some common outcomes between A and B, because otherwise, at least one of the probabilities would be zero.
3. In this case, since both P(A) and P(B) are greater than zero, events A and B cannot be disjoint.
Therefore, it is not possible for events A and B to be disjoint based on the given probabilities.