The sample space for a roll of two number cubes is shown in the table. What is the probability that the roll will result in two even numbers? (1,1)|(1,2)|(1,3)|(1,4)|(1,5),(1,6) (2,1)|(2,2)|(2,3)|(2,4)|(2,5)|(2,6) (3,1)|(3,2)|(3,3)|(3,4)|(3,5)|(3,6) (4,1)|(4,2)|(4,3)|(4,4)|(4,5)|(4,6) (5,1)|(5,2)|(5,3)|(5,4)|(5,5)|(5,6) (6,1)|(6,2)|(6,3)|(6,5)|(6,5)|(6,6)
There are 36 possible outcomes (6 choices for the first cube and 6 choices for the second cube).
To get two even numbers, we need the first cube to land on an even number (choices: 2, 4, 6) and the second cube to also land on an even number (choices: 2, 4, 6).
There are 3 even choices for the first cube and 3 even choices for the second cube, so there are a total of 3 x 3 = 9 outcomes where both cubes are even.
So the probability of rolling two even numbers is 9/36, which simplifies to 1/4 or 25%.
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To find the probability that the roll will result in two even numbers, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
Step 1: Count the favorable outcomes
In this case, the favorable outcomes are any rolls where both numbers are even. Looking at the table, we can count the following favorable outcomes:
- (2,2)
- (2,4)
- (2,6)
- (4,2)
- (4,4)
- (4,6)
- (6,2)
- (6,4)
- (6,6)
So, there are 9 favorable outcomes.
Step 2: Count the total number of possible outcomes
To count the total number of possible outcomes, we can see that there are 6 possible outcomes for each roll of the first number cube (since it has numbers 1 to 6), and similarly, there are 6 possible outcomes for each roll of the second number cube. Thus, the total number of possible outcomes is 6 * 6 = 36.
Step 3: Calculate the probability
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 9 / 36
Probability = 1/4
Therefore, the probability that the roll will result in two even numbers is 1/4 or 25%.