Suppose a die is rolled and the possible outcomes are {1, 2, 3, 4, 5, 6}. Let Event A be the event that the outcome is an odd number, and Event B be the event that the outcome is less than 4. Are Events A and B mutually exclusive?
Answer
For two events to be mutually exclusive, they cannot have any outcomes in common. However, A and B both include the outcomes 1 and 3, so they are not mutually exclusive.
Step 1 ：The sample space \(S\) of the experiment is \(S = \{1, 2, 3, 4, 5, 6\}\)
Step 2 ：Event A is the event that the outcome is an odd number, so \(A = \{1, 3, 5\}\)
Step 3 ：Event B is the event that the outcome is less than 4, so \(B = \{1, 2, 3\}\)
Step 4 ：For two events to be mutually exclusive, they cannot have any outcomes in common. However, A and B both include the outcomes 1 and 3, so they are not mutually exclusive.
