Question

question 1

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

getting a prime number
getting a number greater than 5

getting a prime number
getting a number less than 2

getting an odd number
getting a number less than 4

getting a 4
getting an odd number

Explanation:

Define overlapping events

Using the Mutually Exclusive Events knowledge point

Two events are overlapping (not mutually exclusive) if they can occur at the same time, meaning their intersection is non-empty:

$$ A \cap B eq \emptyset $$

Define the sample space

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

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

Analyze each option

Using the Mutually Exclusive Events knowledge point

• Option 1:
• Prime numbers: \(P = \{2, 3, 5\}\)
• Numbers greater than 5: \(G = \{6\}\)
• Intersection: \(P \cap G = \emptyset\) (Mutually exclusive)

• Option 2:
• Prime numbers: \(P = \{2, 3, 5\}\)
• Numbers less than 2: \(L = \{1\}\)
• Intersection: \(P \cap L = \emptyset\) (Mutually exclusive)

• Option 3:
• Odd numbers: \(O = \{1, 3, 5\}\)
• Numbers less than 4: \(T = \{1, 2, 3\}\)
• Intersection: \(O \cap T = \{1, 3\}\) (Overlapping)

• Option 4:
• Getting a 4: \(F = \{4\}\)
• Odd numbers: \(O = \{1, 3, 5\}\)
• Intersection: \(F \cap O = \emptyset\) (Mutually exclusive)

Identify the correct pair

The only pair of events that share common outcomes (overlap) is getting an odd number and getting a number less than 4, as both events contain the outcomes 1 and 3.

Answer:

• Getting a prime number / Getting a number greater than 5
• Getting a prime number / Getting a number less than 2
• Getting an odd number / Getting a number less than 4 (Correct answer)
• Getting a 4 / Getting an odd number