Suppose there are 8 red tiles, 10 blue tiles, and 2 green tiles in a bag.

The probability of randomly selecting a red or blue tile is given by:
[tex]\[ \frac{8}{20} + \frac{10}{20} = \frac{18}{20} \][/tex]

Starting over with the same bag, what is the probability of getting a blue tile or a green tile?

A. [tex]$\frac{14}{20}$[/tex]

B. [tex]$\frac{12}{20}$[/tex]

C. [tex]$\frac{4}{20}$[/tex]

To solve the question of finding the probability of randomly selecting a blue tile or a green tile from the bag, follow these steps:

1. Identify the Total Number of Tiles:
- There are 8 red tiles, 10 blue tiles, and 2 green tiles.
- Add these together to find the total number of tiles:
[tex]\[
8 + 10 + 2 = 20
\][/tex]
- So, there are 20 tiles in total.

2. Find the Number of Blue Tiles and Green Tiles:
- You have 10 blue tiles.
- You have 2 green tiles.

3. Calculate the Probability of Selecting a Blue Tile:
- The probability formula for an event is the number of favorable outcomes divided by the total number of possible outcomes.
- Therefore, the probability of selecting a blue tile is:
[tex]\[
\frac{\text{Number of Blue Tiles}}{\text{Total Number of Tiles}} = \frac{10}{20} = 0.5
\][/tex]

4. Calculate the Probability of Selecting a Green Tile:
- Similarly, the probability of selecting a green tile is:
[tex]\[
\frac{\text{Number of Green Tiles}}{\text{Total Number of Tiles}} = \frac{2}{20} = 0.1
\][/tex]

5. Calculate the Probability of Selecting Either a Blue or a Green Tile:
- Since selecting a blue tile and selecting a green tile are mutually exclusive events (they can't happen at the same time), you can add their probabilities together:
[tex]\[
\text{Probability of Blue or Green} = 0.5 + 0.1 = 0.6
\][/tex]

So, the probability of randomly selecting either a blue tile or a green tile from the bag is [tex]$\frac{12}{20}$[/tex] or 0.6.