Using a sixteen-sided number cube, what is the probability that you will roll an even number or an odd prime number? The number 1 isn't an odd prime. Round to three decimals.
First, let's determine the total number of outcomes when rolling a sixteen-sided number cube, which is 16.
Next, let's identify the number of outcomes where we roll an even number or an odd prime number:
- Even numbers on the sixteen-sided cube are 2, 4, 6, 8, 10, 12, and 14 (7 even numbers).
- Odd prime numbers on the sixteen-sided cube are 3, 5, 7, 11, and 13 (5 odd prime numbers).
- Since 2 is counted in the even numbers, we will not count it again as it is not an odd prime.
Therefore, there are 7 even numbers and 5 odd prime numbers, with an overlap of 1 for the number 2.
To find the total number of outcomes where we roll an even number or an odd prime number, we need to add the two sets together and then subtract the overlap:
7 + 5 - 1 = 11
So there are 11 outcomes where we roll an even number or an odd prime number.
Finally, we calculate the probability:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 11 / 16 ≈ 0.688
Therefore, the probability of rolling an even number or an odd prime number on a sixteen-sided number cube is approximately 0.688 or rounded to three decimals: 0.688.