Question

A lecture hall has 200 seats with folding arm tablets, 30 of which are designed for left-handers. The typical size of classes that meet there is 188, and we can assume that about \(13 \%\) 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?

Short answer

0 probability; right-handed students won't need left-handed seats.

Step-by-step solution

Determine the Number of Left-handed Seats

The lecture hall has a total of 200 seats, out of which 30 are designed for left-handed students. These are the special left-handed seats available.

Calculate Expected Number of Left-handed Students

The class size is 188 students, and 13% of them are left-handed. The number of left-handed students can be calculated as follows: \(0.13 \times 188 = 24.44\). Since the number of students must be whole, we round it to 24 left-handed students.

Evaluate Left-handed Seat Occupancy

We have 30 left-handed seats and approximately 24 left-handed students. Since 24 left-handed students will occupy 24 of the 30 left-handed seats, there will still be 6 left-handed seats remaining.

Determine Available Right-handed Seats

Out of the 200 total seats, 170 are for right-handed students (200 total seats - 30 left-handed seats). Since 24 left-handed students occupy left-handed seats, 164 seats remain available for right-handed students.

Calculate Probability of Right-handed Using Lefty Tablet

There are 188 total students and 24 are left-handed, leaving 164 right-handed students. Since there are 164 right-handed seats (with 6 unoccupied left-handed seats still available), all right-handed students will get a right-handed seat without occupying a left-handed seat. Hence, the probability is \(0\).

Key concepts

Right-handed Students

In most environments, right-handed students make up the majority of the class. This is important because seating arrangements often cater primarily to them. Let’s look closer at how right-handedness affects seat selection in a lecture hall.

• Right-handed seats are typically designed with arm tablets on the right side. This is to accommodate the ease of writing for right-handed individuals.
• In our example, of the 200 total seats, there are 170 designed for these students.
• Given that right-handed students derive from the remaining 87% of the class, it’s crucial to ensure they have adequate seating options.

Understanding the proportion of right-handed students ensures there are enough seats for everyone and helps planners avoid uncomfortable situations, like having right-handed students forced to use left-handed arm tablets. In the exercise scenario, with all measures correctly in place, right-handed students end up using right-handed seats without any issue.

Left-handed Students

Left-handed students often face unique challenges in lecture halls due to the limited number of specially designed seats. Here, let’s explore more about the accommodations required for left-handed students.

• Lecture halls should include left-handed seating, typically featuring an arm tablet on the left side. This is crucial for the students’ comfort and effectiveness in writing.
• In the given problem, out of 200 sets, 30 are specifically designed for left-handed students, which is roughly 15% of all seats.
• The exercise tells us approximately 13% of a class, or about 24 students, are left-handed, indicating an adequate number of dedicated seats.

Properly accommodating left-handed students means providing sufficient seating that meets their needs. In our example, the planning leaves 6 left-handed seats unoccupied, offering an excellent balance for these students, preventing any necessity for right-handers to use these seats.

Lecture Hall Seating Arrangement

Seating arrangements in a lecture hall are pivotal for accommodating the various needs of students. Good planning takes into account the proportions of right-handed versus left-handed students.

• Understanding the composition of a class helps assign the right mix of seating after considering statistical or historical data, such as the percentage of left-handed and right-handed individuals.
• The efficient arrangement of seats ensures students are comfortable and not forced into unsuitable seating, potentially affecting their ability to focus and work.
• In the scenario from the exercise, the seating plan provided is near-perfect, with plenty of right-handed seats available for all the right-handed students and an excess of left-handed seats for those students.

Seating arrangements that match student demographics ensure everyone has a seat that caters to their needs. Understanding probability and logistical constraints can help in designing these arrangements more effectively, as seen with zero probability of right-handed students having to use left-handed seats in this well-planned example.