Myra and her friends are playing a board game. On every turn, they roll a die to see how many spaces to move forward. The die is labeled with the numbers 1 to 6. Select all of the true statements.

A. The probability of rolling 0 is 1
B. The probability of rolling an even prime number is 0
C. The probability of rolling an odd number is 1/2
D. The probability of not rolling 6 is 1/6
E. The probability of rolling a multiple or an even number is 5/6
F. The probability of rolling a factor of 9 is 1/3

1 answer

Let's analyze each statement one by one based on a standard six-sided die labeled with numbers 1 to 6.

A. The probability of rolling 0 is 1.

  • False. The die does not have a 0, so the probability of rolling a 0 is 0.

B. The probability of rolling an even prime number is 0.

  • True. The only even prime number is 2, which can be rolled. So the probability of rolling an even prime number is not 0; it is 1/6 (since only the number 2 meets the condition). Therefore, this statement is false.

C. The probability of rolling an odd number is 1/2.

  • True. The odd numbers on the die are 1, 3, and 5. There are 3 odd numbers out of 6 possible outcomes, so the probability is 3/6 = 1/2.

D. The probability of not rolling 6 is 1/6.

  • False. There are 5 outcomes (1, 2, 3, 4, 5) that are not 6 out of 6 total outcomes. Thus, the probability of not rolling a 6 is 5/6.

E. The probability of rolling a multiple or an even number is 5/6.

  • True. The multiples of numbers between 1 and 6 are 1, 2, 3, 4, 5, and 6. The even numbers in that range are 2, 4, and 6. If we combine them, we have every number except for 1 as a multiple or even number. The probability of rolling not 1 is 5/6, which makes this statement true.

F. The probability of rolling a factor of 9 is 1/3.

  • True. The factors of 9 that can be rolled on a die are 1 and 3. There are 2 favorable outcomes (1 and 3) out of a total of 6 possible outcomes, giving us a probability of 2/6, which simplifies to 1/3. Hence, this statement is true.

In summary, the true statements are:

  • C: The probability of rolling an odd number is 1/2.
  • E: The probability of rolling a multiple or an even number is 5/6.
  • F: The probability of rolling a factor of 9 is 1/3.