An electronics company polled 300 random people to find out whether they own cell phones and laptops. The results are shown in the table below.

\begin{tabular}{|c|c|c|c|}
\cline { 2 - 4 }
& Cell Phone & No Cell Phone & Total \\
\hline
Laptop & 82 & 11 & [tex]$b$[/tex] \\
\hline
No Laptop & 159 & [tex]$a$[/tex] & 207 \\
\hline
Total & 241 & 59 & 300 \\
\hline
\end{tabular}

Use the table to complete the statements:
1. The cell labeled [tex]$a$[/tex] is [tex]$\square$[/tex]
2. The cell labeled [tex]$b$[/tex] is [tex]$\square$[/tex]



Answer :

To determine the values in the table, let's analyze the given data step-by-step:

1. Total People:
- The total number of people polled is 300.

2. Total Laptops and Cell Phones:
- The total number of people with laptops is 207.
- The total number of people with cell phones is 241.

3. Particular Values:
- People who own both a laptop and a cell phone: 82
- People who own a laptop but not a cell phone: 11

4. Determine 'a':
- 'a' is the number of people who own a cell phone but not a laptop.
- Since the total number of people is 300, the total number of people without laptops is 300 - 207 = 93.
- Therefore, 'a' represents these 93 people who do not have a laptop but do have a cell phone.

5. Determine 'b':
- 'b' is the total number of people who own a laptop, regardless of whether they have a cell phone.
- This can be determined by adding the number of laptop owners who also own cell phones to the number of laptop owners who do not own cell phones.
- From the table, people with laptops that also own cell phones = 82, and people with laptops that do not own cell phones = 11.
- Thus, 'b' is 82 + 11 = 93.

Using these computations, the completed statements are:

1. The cell labeled 'a' is 82 (number of people with cell phones but not laptops).
2. The cell labeled 'b' is 93 (total number of people with laptops).