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Challenge  Suppose you have a bag with 50 letter tiles in it and 19 of the tiles are the letter Upper T. If you pick a letter tile at random from the​ bag, the probability that it is the letter Upper T is StartFraction 19 Over 50 EndFraction

. Suppose another bag has 500 letter tiles in it and 150 of the tiles are the letter Upper T. Write the probability of picking a tile that is the letter Upper T as a fraction and as a percent. From which bag are you more likely to pick a tile that is the letter Upper T​?
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Part 1
​P(Upper T​) as a fraction is
  
enter your response here.
​(Simplify your​ answer.)

1 answer

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

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

In the second bag, there are 150 T tiles out of a total of 500 tiles. Thus, the probability can be calculated as follows:

\[ P(T) = \frac{150}{500} \]

Next, we simplify the fraction:

\[ P(T) = \frac{150 \div 50}{500 \div 50} = \frac{3}{10} \]

Thus, the probability of picking a tile that is the letter T from the second bag as a fraction is:

\[ \frac{3}{10} \]

Now, let's also express this probability as a percent. To convert the fraction to a percent, we multiply by 100:

\[ P(T) \text{ (as a percent)} = \frac{3}{10} \times 100 = 30% \]

Summary:

  1. Probability of picking T from the second bag as a fraction: \(\frac{3}{10}\)
  2. Probability of picking T from the second bag as a percent: \(30%\)

Comparing the Two Bags:

  • First bag: \(P(T) = \frac{19}{50} = 0.38 = 38%\)
  • Second bag: \(P(T) = \frac{3}{10} = 0.30 = 30%\)

From this comparison, you are more likely to pick a tile that is the letter T from the first bag since \(38%\) is greater than \(30%\).