A lecture hall has 200 seats with folding arm​ tablets, 33 of which are designed for​ left-handers. The average size of classes that meet there is 187​, and we can assume that about 12​% of students are​ left-handed. What's the probability that a​ right-handed student in one of these classes is forced to use a lefty arm​ tablet?
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Part 1
The probability that a​ right-handed student in one of these classes is forced to use a lefty arm tablet is 
  
enter your response here. ​(Round to four decimal places as​ needed.)

To solve this problem, let’s break it down step-by-step:

1. **Total Seats**: There are 200 seats in the lecture hall, 33 of which have left-handed arm tablets. Therefore, 200 - 33 = 167 seats have right-handed arm tablets.

2. **Class Size and Left-Handed Students**: The class size is 187 students, and 12% of them are assumed to be left-handed. The number of left-handed students is:
   \[
   0.12 \times 187 = 22.44 \approx 22 \text{ (rounding to the nearest whole number)}
   \]

   Thus, we assume there are about 22 left-handed students in the class.

3. **Left-Handed Seats Usage**: Since there are 22 left-handed students and 33 left-handed arm tablet seats, there are enough left-handed seats for the left-handed students, leaving:
   \[
   33 - 22 = 11 \text{ left-handed seats unoccupied by left-handed students}
   \]

4. **Remaining Seats for Right-Handed Students**: There are 187 - 22 = 165 right-handed students in the class. With only 167 right-handed seats available, the 165 right-handed students would generally be able to use these seats. However, since 167 - 165 = 2 right-handed seats would still remain available, there’s no need for any right-handed students to be forced into a left-handed arm tablet seat.

### Final Answer:
The probability that a right-handed student in one of these classes is forced to use a left-handed arm tablet is:
\[
0
\]

Would you like more details, or do you have any questions?

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Here are five related questions to deepen understanding:

1. What would the probability be if there were fewer right-handed seats available?
2. How would the result change if the percentage of left-handed students were higher?
3. If the lecture hall increased in size to accommodate more seats, how would that affect this probability?
4. How many additional left-handed seats would be required to reduce this probability further in a larger class?
5. What if the class size exceeded the total seats in the hall? How would probability be calculated?

**Tip**: In probability problems, clearly separating groups and determining which are over- or under-resourced often simplifies calculations and reduces errors.

A lecture hall has 200 seats with folding arm tablets, 33 of which are designed for left-handers. The average size of classes that meet there is 187, and we can assume that about 12% of students are left-handed. What's the probability that a right-handed student in one of these classes is forced to use a lefty arm tablet?

Solve the probability problem of a right-handed student using a left-handed tablet in a lecture hall with 200 seats, 33 of which are for left-handers. Given a class size of 187 and a left-handed population of 12%, this problem walks through each step with key probability and combinatorics concepts. Ideal for Grades 10-12.

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