Answer :
To determine the probability that both number cubes come up even when Martha rolls two number cubes, let's go through the solution step-by-step:
1. Identify the total number of sides on a number cube and the even numbers:
A standard number cube (die) has 6 sides with the numbers: 1, 2, 3, 4, 5, and 6. Out of these numbers, the even numbers are 2, 4, and 6.
2. Calculate the probability of rolling an even number on one cube:
There are 3 even numbers out of 6 possible numbers on a single cube. Therefore, the probability of rolling an even number on one cube is:
[tex]\[ \frac{3}{6} = \frac{1}{2} \][/tex]
3. Determine the probability of both cubes showing even numbers:
Since the rolls of the two number cubes are independent events, the joint probability of both events happening (both cubes showing even numbers) is the product of the probabilities of each event. Thus, the probability of both cubes showing even numbers is:
[tex]\[ \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \frac{1}{4} \][/tex]
4. Conclusion:
The probability that both number cubes come up even is \( \frac{1}{4} \).
Therefore, the answer is:
[tex]\[ \boxed{\frac{1}{4}} \][/tex]
So, the correct choice is:
A) [tex]\(\frac{1}{4}\)[/tex]
1. Identify the total number of sides on a number cube and the even numbers:
A standard number cube (die) has 6 sides with the numbers: 1, 2, 3, 4, 5, and 6. Out of these numbers, the even numbers are 2, 4, and 6.
2. Calculate the probability of rolling an even number on one cube:
There are 3 even numbers out of 6 possible numbers on a single cube. Therefore, the probability of rolling an even number on one cube is:
[tex]\[ \frac{3}{6} = \frac{1}{2} \][/tex]
3. Determine the probability of both cubes showing even numbers:
Since the rolls of the two number cubes are independent events, the joint probability of both events happening (both cubes showing even numbers) is the product of the probabilities of each event. Thus, the probability of both cubes showing even numbers is:
[tex]\[ \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \frac{1}{4} \][/tex]
4. Conclusion:
The probability that both number cubes come up even is \( \frac{1}{4} \).
Therefore, the answer is:
[tex]\[ \boxed{\frac{1}{4}} \][/tex]
So, the correct choice is:
A) [tex]\(\frac{1}{4}\)[/tex]
