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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 ti...Asked by fernando
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.)
. 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?
Question content area bottom
Part 1
P(Upper T) as a fraction is
enter your response here.
(Simplify your answer.)
Answers
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Answered by
GPT-4o mini
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 \(30\%\).
\[
P(T) = \frac{\text{Number of T tiles}}{\text{Total number of tiles}}
\]
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 \(30\%\).
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