Question

in an experiment, a die is tossed. are these events mutually exclusive or overlapping?

event a: it lands on 4
event b: it lands on a number less than 3

mutually exclusive

overlapping

Explanation:

Define the sample space

The sample space \(S\) for tossing a standard six-sided die is:

$$ S = \{1, 2, 3, 4, 5, 6\} $$

Identify outcomes for Event A

Using the Mutually Exclusive Events and Overlapping Events knowledge points

$$ A = \{4\} $$

Identify outcomes for Event B

Using the Mutually Exclusive Events and Overlapping Events knowledge points

$$ B = \{1, 2\} $$

Find the intersection of A and B

Using the Mutually Exclusive Events and Overlapping Events knowledge points

$$ A \cap B = \{4\} \cap \{1, 2\} = \emptyset $$

Determine if events are mutually exclusive

Using the Mutually Exclusive Events and Overlapping Events knowledge points
Since \(A \cap B = \emptyset\), the events cannot occur at the same time.

Answer:

• mutually exclusive (Correct answer)
• overlapping