Suppose you roll a red number cube and a yellow number cube.
What is the probability of rolling any matching pair of numbers? (Hint: Add the probability of each of the six matches.)
To find the probability of rolling any matching pair of numbers, we need to add the probabilities of each of the six possible matches.
First, let's determine the total number of possible outcomes when rolling the two number cubes. Since there are six numbers on each cube (1, 2, 3, 4, 5, 6), there are a total of 6 * 6 = 36 possible outcomes.
Now, let's calculate the probability of each matching pair. There are six possible matching pairs: (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), and (6, 6).
The probability of rolling a specific pair, let's say (1, 1), can be calculated by multiplying the individual probabilities of rolling a 1 on each cube. Since each number cube has six equally likely outcomes, the probability of rolling a 1 on either cube is 1/6. Therefore, the probability of rolling (1, 1) is (1/6) * (1/6) = 1/36.
Similarly, the probability of rolling any of the remaining matching pairs is also 1/36.
Finally, to find the probability of rolling any matching pair, we add the probabilities of each of the six matches:
(1/36) + (1/36) + (1/36) + (1/36) + (1/36) + (1/36) = 6/36 = 1/6.
Therefore, the probability of rolling any matching pair of numbers is 1/6.
To determine the probability of rolling any matching pair of numbers, we need to consider the possible outcomes of rolling the red and yellow number cubes.
The red number cube can show any number from 1 to 6, and the yellow number cube can also show any number from 1 to 6.
There are a total of 6 possible outcomes for each cube. To find the probability of rolling any matching pair of numbers, we need to count the number of matching pairs and divide it by the total number of possible outcomes.
There are six possible matching pairs:
1. Both cubes show 1
2. Both cubes show 2
3. Both cubes show 3
4. Both cubes show 4
5. Both cubes show 5
6. Both cubes show 6
Since there are only 6 possible matching pairs and a total of 6 x 6 = 36 possible outcomes, the probability of rolling any matching pair of numbers is 6/36 = 1/6.
So the probability of rolling any matching pair of numbers is 1/6.
The cube has 6 faces, so 6 outcomes.
When two different dice are thrown, there are a total of 6*6=36 outcomes.
You can make a table of the 36 outcomes and find out how many of them are the same (6 out of 36).
Alternatively, you can think of the red cube is thrown first with any of the 6 possible outcomes. The yellow cube that is thrown (1 millionth of a second later) has a 1/6 probability of matching the red.