a red and blue number cube are rolled. determine the probability that an odd number is rolled on the red cube and a number greater than 1 is rolled on the blue cube
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
P(red) = 3/6
P(blue) = 5/6
To determine the probability, we need to find the number of favorable outcomes (the outcomes that meet the criteria) and divide it by the number of possible outcomes.
First, let's identify the outcomes for the red cube. The red cube has six faces, numbered 1 to 6. The odd numbers on the red cube are 1, 3, and 5.
Next, let's identify the outcomes for the blue cube. The blue cube also has six faces, numbered 1 to 6. The numbers greater than 1 on the blue cube are 2, 3, 4, 5, and 6.
To find the favorable outcomes, we need to find the common outcomes that satisfy both criteria: an odd number on the red cube and a number greater than 1 on the blue cube.
The common outcomes are:
- Red: 1, Blue: 2
- Red: 1, Blue: 3
- Red: 1, Blue: 4
- Red: 1, Blue: 5
- Red: 1, Blue: 6
- Red: 3, Blue: 2
- Red: 3, Blue: 3
- Red: 3, Blue: 4
- Red: 3, Blue: 5
- Red: 3, Blue: 6
- Red: 5, Blue: 2
- Red: 5, Blue: 3
- Red: 5, Blue: 4
- Red: 5, Blue: 5
- Red: 5, Blue: 6
Therefore, we have 15 favorable outcomes.
Since each cube has 6 possible outcomes, the total number of possible outcomes is 6 * 6 = 36.
To find the probability, we divide the number of favorable outcomes by the number of possible outcomes:
Probability = Favorable outcomes / Total outcomes
Probability = 15 / 36
Probability = 5 / 12
So, the probability that an odd number is rolled on the red cube and a number greater than 1 is rolled on the blue cube is 5/12.
To determine the probability, we need to know the number of favorable outcomes and the total number of possible outcomes.
Let's first consider the favorable outcomes for each cube individually:
1. For the red cube, the favorable outcomes are odd numbers. Odd numbers on a standard number cube are 1, 3, and 5. So, there are 3 favorable outcomes for the red cube.
2. For the blue cube, the favorable outcomes are numbers greater than 1. These include 2, 3, 4, 5, and 6. So, there are 5 favorable outcomes for the blue cube.
Now, let's determine the total number of possible outcomes:
Since there are 6 sides on a standard number cube, the total number of possible outcomes for each cube is 6.
To find the total number of possible outcomes when rolling both cubes together, we multiply the number of outcomes for each cube. So, the total number of possible outcomes is 6 * 6 = 36.
Now we can determine 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)
= (3 * 5) / 36
= 15 / 36
Simplifying the fraction, the probability is 5/12.