Math Problem Statement

Which pair of events are NOT overlapping when rolling a single six-sided die?

A.)Getting a number greater than 2 Getting a number less than 5

B.)Getting an odd number Getting a prime number

C.)Getting a number greater than 4 Getting a number less than 2

D.)Getting an even number Getting a prime number

Solution

To identify which pair of events are NOT overlapping when rolling a six-sided die, we need to check if the two events in each pair have any outcomes in common.

Let’s analyze each option:

A) Getting a number greater than 2 and Getting a number less than 5

  • Getting a number greater than 2: {3, 4, 5, 6}
  • Getting a number less than 5: {1, 2, 3, 4}
  • Overlap: {3, 4}

These events do overlap because both 3 and 4 are in common.

B) Getting an odd number and Getting a prime number

  • Odd numbers: {1, 3, 5}
  • Prime numbers (on a die): {2, 3, 5}
  • Overlap: {3, 5}

These events do overlap because 3 and 5 are in common.

C) Getting a number greater than 4 and Getting a number less than 2

  • Getting a number greater than 4: {5, 6}
  • Getting a number less than 2: {1}
  • Overlap: None

These events do not overlap, as there are no numbers common between {5, 6} and {1}.

D) Getting an even number and Getting a prime number

  • Even numbers: {2, 4, 6}
  • Prime numbers: {2, 3, 5}
  • Overlap: {2}

These events do overlap because the number 2 is in common.


Conclusion:

The correct answer is: C) Getting a number greater than 4 and Getting a number less than 2

These events do not overlap, as they have no numbers in common.

Would you like more details or have any other questions?

5 Related Questions:

  1. What are mutually exclusive events in probability?
  2. Can two events overlap if they are independent?
  3. How do you calculate the probability of non-overlapping events?
  4. What are examples of overlapping events in real-life scenarios?
  5. How do you represent overlapping events using Venn diagrams?

Tip:

Non-overlapping events, also called mutually exclusive events, have no common outcomes and their intersection is empty.

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Math Problem Analysis

Mathematical Concepts

Probability
Mutually Exclusive Events
Overlapping Events

Formulas

None required for this problem, but intersections of sets are relevant

Theorems

Mutually Exclusive Events

Suitable Grade Level

Grades 6-8