Question

You randomly choose one of the tiles. Without replacing the first tile, you randomly choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth.The probability of choosing a red tile and then a vowel is

Answer 1

I can’t see the image

Answer 2

The probability of choosing a red tile and then a vowel is approximately 4.8%.

To find the probability of choosing a red tile and then a vowel without replacement, we'll follow these steps:

1. Determine the total number of tiles.

2. Find the number of red tiles.

3. Calculate the probability of picking a red tile first.

4. Determine the total number of vowels on the tiles.

5. Calculate the probability of picking a vowel after a red tile has been picked.

6. Multiply the probabilities from steps 3 and 5 to get the compound probability.

From the image, we can identify the tiles and their colors:

• Red Tiles: G
• Blue Tiles: A, K, Q
• Green Tiles: D, R, E

There are a total of 7 tiles.

Step 1: The total number of tiles is 7.

Step 2: There is 1 red tile (G).

Step 3: The probability of picking the red tile first is 1/7.

Step 4: The vowels among the tiles are A and E. There are 2 vowels.

Step 5: After removing the red tile, there are 6 tiles left. The probability of then picking a vowel is 2/6, which simplifies to 1/3.

Step 6: The compound probability is the product of the two probabilities:

P(red tile and then a vowel) = P(red first) × P(vowel second)

P(red tile and then a vowel) =
`(1)/(7) * (1)/(3)`

P(red tile and then a vowel) =
`(1)/(21)`

Now, we'll convert this fraction to a percent rounded to the nearest tenth.

`\[ (1)/(21) \approx 0.0476... \]`

To convert to a percent:

`\[ 0.0476... * 100 \approx 4.8\% \]`

The answer is approximately 4.8%.