Question

A popular word game starts with 100 letter tiles in a bag. The table shows the distribution for the vowels l.
Vowel A E I O U
Number of Tiles 9 12 9 8 4
What is the probability that a vowel is selected on the first draw?

Answer 1

To find the probability of selecting a vowel on the first draw from the bag of letter tiles, we need to determine the total number of vowels and the total number of tiles.

From the table, we calculate the total number of vowels as follows:

- Number of A tiles = 9
- Number of E tiles = 12
- Number of I tiles = 9
- Number of O tiles = 8
- Number of U tiles = 4

Now we add these numbers together:

\[
\text{Total number of vowels} = 9 + 12 + 9 + 8 + 4 = 42
\]

The total number of tiles is given as 100.

Now, the probability \( P \) of drawing a vowel on the first draw is given by the formula:

\[
P(\text{vowel}) = \frac{\text{Number of vowels}}{\text{Total number of tiles}} = \frac{42}{100}
\]

Simplifying this fraction:

\[
P(\text{vowel}) = \frac{21}{50}
\]

Therefore, the probability that a vowel is selected on the first draw is \( \frac{21}{50} \), or 0.42 when expressed as a decimal.