If you roll a standard number cube, determine the probability that you roll an even number or a 5.(1 point)

Responses

112
Start Fraction 1 over 12 End Fraction

12
Start Fraction 1 over 2 End Fraction

16
Start Fraction 1 over 6 End Fraction

23
Start Fraction 2 over 3 End Fraction

1 answer

A standard number cube (or die) has the numbers 1 through 6. We need to determine the probability of rolling an even number or a 5.

  1. Identify the even numbers on a die: The even numbers are 2, 4, and 6. This gives us a total of 3 even numbers.
  2. Identify the number 5: This is 1 additional outcome.

Now, let's list the favorable outcomes:

  • Even numbers: 2, 4, 6 (3 outcomes)
  • The number 5: 5 (1 outcome)

Now we can count the total unique favorable outcomes:

  • The even numbers are 2, 4, and 6.
  • The number 5 adds 1 outcome.

Thus, the favorable outcomes are: 2, 4, 5, 6 (or a total of 4 favorable outcomes: 2, 4, 5, 6).

  1. Total outcomes when rolling a die: There are a total of 6 possible outcomes (1, 2, 3, 4, 5, 6).

  2. Calculate the probability: \[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{4}{6} = \frac{2}{3} \]

Thus, the probability that you roll an even number or a 5 is \(\frac{2}{3}\).

The correct answer is: \[ \frac{2}{3} \]