Question

question 24

which pair of events are non-overlapping when rolling a single six-sided die?

getting an even number
getting an odd number

getting a number greater than 4
getting a 5

getting a greater than 2
getting a number less than 4

getting a number less than 3
getting a prime number

Explanation:

Define the sample space and events

Using the Overlapping Events knowledge point

The sample space for rolling a single six-sided die is:

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

Non-overlapping (mutually exclusive) events are events that cannot occur at the same time. This means their intersection is empty:

$$ A \cap B = \emptyset $$

Analyze the first option

Using the Overlapping Events knowledge point

Let \(A\) be the event of getting an even number, and \(B\) be the event of getting an odd number:

$$ A = \{2, 4, 6\} $$

$$ B = \{1, 3, 5\} $$

Find the intersection:

$$ A \cap B = \{2, 4, 6\} \cap \{1, 3, 5\} = \emptyset $$

Since there are no common outcomes, these events are non-overlapping.

Analyze the second option

Using the Overlapping Events knowledge point

Let \(C\) be the event of getting a number greater than 4, and \(D\) be the event of getting a 5:

$$ C = \{5, 6\} $$

$$ D = \{5\} $$

Find the intersection:

$$ C \cap D = \{5\} e \emptyset $$

These events are overlapping.

Analyze the third option

Using the Overlapping Events knowledge point

Let \(E\) be the event of getting a number greater than 2, and \(F\) be the event of getting a number less than 4:

$$ E = \{3, 4, 5, 6\} $$

$$ F = \{1, 2, 3\} $$

Find the intersection:

$$ E \cap F = \{3\} e \emptyset $$

These events are overlapping.

Analyze the fourth option

Using the Overlapping Events knowledge point

Let \(G\) be the event of getting a number less than 3, and \(H\) be the event of getting a prime number:

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

$$ H = \{2, 3, 5\} $$

Find the intersection:

$$ G \cap H = \{2\} e \emptyset $$

These events are overlapping.

Answer:

• **Getting an even number

Getting an odd number (Correct answer)**

• Getting a number greater than 4

Getting a 5

• Getting a greater than 2

Getting a number less than 4

• Getting a number less than 3

Getting a prime number