Question

Challenge  Suppose you have a bag with 50 letter tiles in it and 13 of the tiles are the letter Upper Z. If you pick a letter tile at random from the​ bag, the probability that it is the letter Upper Z is StartFraction 13 Over 50 EndFraction
. Suppose another bag has 200 letter tiles in it and 112 of the tiles are the letter Upper Z. Write the probability of picking a tile that is the letter Upper Z as a fraction and as a percent. From which bag are you more likely to pick a tile that is the letter Upper Z​?
Question content area bottom
Part 1
​P(Upper Z​) as a fraction is
  
enter your response here.
​(Simplify your​ answer.)

Answer 1

To find the probability of picking a tile that is the letter Z from the second bag, you can use the formula for probability:

\[
P(\text{Upper Z}) = \frac{\text{Number of Upper Z tiles}}{\text{Total number of tiles}}.
\]

Given that there are 112 Upper Z tiles in the second bag out of a total of 200 tiles, the probability can be calculated as:

\[
P(\text{Upper Z}) = \frac{112}{200}.
\]

Now, let's simplify this fraction. Both the numerator and denominator can be divided by 8:

\[
\frac{112 \div 8}{200 \div 8} = \frac{14}{25}.
\]

So, the probability \( P(\text{Upper Z}) \) as a fraction is:

\[
\frac{14}{25}.
\]

Next, to convert this fraction into a percentage, you multiply by 100:

\[
P(\text{Upper Z}) = \frac{14}{25} \times 100 = 56\%.
\]

Therefore, the probability of picking a tile that is the letter Z from the second bag can be expressed as:

- As a fraction: \(\frac{14}{25}\)
- As a percent: \(56\%\)

### Comparison of Both Bags:
1. **First Bag Probability**: \(\frac{13}{50} = 26\%\)
2. **Second Bag Probability**: \(\frac{14}{25} = 56\%\)

You are more likely to pick a tile that is the letter Z from the **second bag** since \(56\%\) is greater than \(26\%\).