Question

determine whether the statement is true or false. if it is false, rewrite it as a true statement.

if two events are mutually exclusive, they have no outcomes in common.

choose the correct answer below.

a. false. if two events are mutually exclusive, they have every outcome in common.
b. false. if two events are mutually exclusive, they have some outcomes in common.
c. true.

Explanation:

Define mutually exclusive events

Using the Mutually Exclusive Events knowledge point

$$ A \cap B = \emptyset $$

Analyze the given statement

Using the Mutually Exclusive Events knowledge point

• The statement is: "If two events are mutually exclusive, they have no outcomes in common."
• Since \(A \cap B = \emptyset\), they share zero outcomes.
• Thus, the statement is true.

Evaluate the multiple-choice options

Using the Mutually Exclusive Events knowledge point

• Option A states the statement is false, which is incorrect.
• Option B states the statement is false, which is incorrect.
• Option C states the statement is true, which is correct.

Answer:

• A. False. If two events are mutually exclusive, they have every outcome in common.
• B. False. If two events are mutually exclusive, they have some outcomes in common.
• C. True. (Correct answer)