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Challenge  Suppose you have a bag with 25 letter tiles in it and 8 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 8 Over 25 EndFraction

. Suppose another bag has 300 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 Upper T from the second bag, we use the same formula for probability:

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

For the second bag:

  • Number of Upper T tiles = 150
  • Total number of tiles = 300

Now we can compute the probability:

\[ P(\text{Upper T}) = \frac{150}{300} \]

Next, we simplify the fraction:

\[ \frac{150}{300} = \frac{1}{2} \]

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

\[ \frac{1}{2} \]

To convert this into a percentage, you multiply the fraction by 100:

\[ P(\text{Upper T}) = \frac{1}{2} \times 100 = 50% \]

Now, comparing the two bags:

  • Probability from the first bag: \(\frac{8}{25} = 0.32\) (or 32%)
  • Probability from the second bag: \(\frac{1}{2} = 0.50\) (or 50%)

Thus, you are more likely to pick a tile that is the letter Upper T from the second bag.