In a bag with plastic shapes, there are 6 triangles, 4 circles, and 5 squares. What is the probability of pulling out two triangles if the first shape is replaced before the second shape is pulled out? Write your answer as a simplified fraction
First, let's calculate the probability of pulling out one triangle.
The total number of shapes in the bag is 6 triangles + 4 circles + 5 squares = 15 shapes.
The probability of pulling out a triangle is therefore 6 triangles / 15 shapes = 2/5 (since 6/15 simplifies to 2/5).
Since the shape is replaced before the second shape is pulled out, the probability of pulling out a second triangle is also 2/5.
To find the probability of both events happening, we multiply the probabilities together:
(2/5) * (2/5) = 4/25.
Therefore, the probability of pulling out two triangles when the first shape is replaced is 4/25.
How many outcomes are in the sample space of rolling two number cubes labeled 1–6? Use the method of your choice.
The sample space is the set of all possible outcomes of rolling two number cubes labeled 1-6. To find the number of outcomes, we multiply the number of outcomes for each individual cube.
Since each number cube has 6 sides, there are 6 possible outcomes for the first cube and 6 possible outcomes for the second cube. Therefore, the total number of outcomes in the sample space is 6 * 6 = 36.
If the sample space for an experiment contains the odd numbers from 1 to 20, how many outcomes will be included in the event “less than 12”?
To determine the number of outcomes in the event "less than 12," we need to count the odd numbers between 1 and 12.
The odd numbers between 1 and 12 are: 1, 3, 5, 7, 9, 11.
Therefore, the event "less than 12" contains 6 outcomes.
Complete the sample space shown in the table for the compound event of rolling a number cube and spinning a spinner that is split into three equally colored sections (red (R), blue (B), and yellow (Y)). Ensure the letter corresponding to the colored section of the spinner is capitalized in your responses. (2 points
To complete the sample space table for the compound event of rolling a number cube and spinning a spinner, we list all the possible outcomes by combining the numbers on the number cube with the colors on the spinner.
Here is the completed sample space table:
| Number Cube (Roll) | Spinner (Spin) |
|--------------------|----------------|
| 1R | 1B |
| 1R | 1R |
| 1R | 1Y |
| 2R | 2B |
| 2R | 2R |
| 2R | 2Y |
| 3R | 3B |
| 3R | 3R |
| 3R | 3Y |
| 4R | 4B |
| 4R | 4R |
| 4R | 4Y |
| 5R | 5B |
| 5R | 5R |
| 5R | 5Y |
| 6R | 6B |
| 6R | 6R |
| 6R | 6Y |
In the table, the letter 'R' represents red on the spinner, the letter 'B' represents blue, and the letter 'Y' represents yellow. The numbers from 1 to 6 on the number cube correspond to the numbers on the spinner.