Question at position 6 The contingency table below represents employees of a communications company classified by age and field of expertise. What is the probability that a randomly selected employee age 35-44 years old has business expertise? (NOTE: Please provide your calculation and final answer in separate blank spaces.) Calculation is: Question Blank 1 of 2[input] Final answer is: Question Blank 2 of 2[input]
[table]
| Under 35 | 35-44 | 45+ | Total Engineering | 8,399 | 8,663 | 7,072 | 24,134 Business | 14,515 | 14,988 | 26,683 | 56,186 Education | 6,738 | 5,657 | 8,669 | 21,064 Liberal Arts | 11,415 | 11,484 | 12,111 | 35,010 Total | 41,067 | 40,792 | 54,535 | 136,394
[/table]

Question

Question at position 6 The contingency table below represents employees of a communications company classified by age and field of expertise. What is the probability that a randomly selected employee age 35-44 years old has business expertise? (NOTE: Please provide your calculation and final answer in separate blank spaces.) Calculation is: Question Blank 1 of 2[input] Final answer is: Question Blank 2 of 2[input] ​
[table]
| Under 35 | 35-44 | 45+ | Total Engineering | 8,399 | 8,663 | 7,072 | 24,134 Business | 14,515 | 14,988 | 26,683 | 56,186 Education | 6,738 | 5,657 | 8,669 | 21,064 Liberal Arts | 11,415 | 11,484 | 12,111 | 35,010 Total | 41,067 | 40,792 | 54,535 | 136,394
[/table]

BlackTom AI · Accepted Answer

Let’s restate the problem to ensure we’re analyzing the right data: we want the probability that a randomly selected employee who is aged 35–44 has business expertise, given the contingency table.
First, identify the relevant totals:
- The number of employees aged 35–44 with business expertise is 14,988 (the intersection of the 35–44 column and the Business row).
- The total number of employees aged 35–44 across all fields is 40,792 (the sum of the 35–44 column: Engineering 8,663 + Business 14,988 + Education 5,657 + Liberal Arts 11,484 = 40,792).
Now, compute the conditional probability: P(Business | Age 35–44) = (number with Business and age 35–44) / (total number aged 35–44).
Option 1 presents the fraction form: 14988 / 40792. This is exactly the required ratio and aligns with the definition above.
Option 2 presents the decimal form: 0.3674. Converting the fraction 14988/40792 to a decimal gives a value around 0.3674 (rounded to four decimal places), so this decimal is simply the numerical approximation of the same probability.
Common misconceptions to watch for:
- Using the wrong age group total (for example, totaling by field across all ages) would lead to an incorrect denominator.
- Mixing up the row and column: the numerator comes from the Business row at the 35–44 column, while the denominator comes from the 35–44 column total across all fields, not the Business row total.
- Assuming a whole-number percentage or an incorrect rounding could misrepresent the probability; decimals should be rounded consistently if required.
In sum, both representations convey the same probability: the fraction 14988/40792 and its decimal equivalent approximately 0.3674.

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