Question

Which two of the events below are mutually exclusive if a fair six- sided dice is rolled once?

a. Rolling a factor of 12
b. Rolling an even number
c. Rolling a prime number
d. Rolling a square number

Answer 1

Upon analyzing the events, we find that 'rolling an even number' and 'rolling a prime number' are not mutually exclusive as they both include the result 2. However, 'rolling a prime number' and 'rolling a square number' are mutually exclusive events as they have no common outcomes when rolling a six-sided die.

Step-by-step explanation:

To determine which events are mutually exclusive when rolling a fair six-sided die, let's analyze each event:

• Rolling a factor of 12: The factors of 12 that are possible on a six-sided die are 1, 2, 3, 4, and 6.
• Rolling an even number: The event includes rolling a 2, 4, or 6.
• Rolling a prime number: The event includes rolling a 2, 3, or 5.
• Rolling a square number: The square numbers on a six-sided die are 1 and 4.

Looking at the events:

• Rolling a factor of 12 and rolling an even number are not mutually exclusive because they both can result in rolling a 2, 4, or 6.
• Rolling a prime number and rolling a square number are not mutually exclusive, as rolling a 2 is common between them.

Therefore, events that are mutually exclusive must not have any common results. Here, rolling an even number (2, 4, 6) and rolling a prime number (2, 3, 5) share the number 2; thus, they are not mutually exclusive. However, rolling a prime number (2, 3, 5) and rolling a square number (1, 4) do not share any common outcomes, implying that they are mutually exclusive.