Question

Difficulty: MediumTwo-Way Tables and Probability

A technology company surveyed a random sample of 128128 of its employees to determine their primary operating system and their job role. The table below summarizes the results of the survey.

Job RolemacOSWindowsTotal
Developer303050508080
Designer303018184848
Total60606868128128

If an employee from the survey whose job role is developer is selected at random, what is the probability that the employee's primary operating system is Windows?

Answer: 0.625

Answer

5/8 (or 0.625)
The question asks for the probability that a randomly selected employee uses Windows, given that their job role is developer. This restricts the sample space to only the developers. From the table, there are 8080 total developers, which serves as the denominator. Within this group of developers, 5050 use Windows, which serves as the numerator. The probability is 5080\frac{50}{80}, which simplifies to 58\frac{5}{8} or 0.6250.625. Both 5/85/8 and .625.625 are correct formats that fit the standard SAT grid-in requirements.

Step-by-Step Solution

1
Identify the subgroup defined by the condition.
The total number of developers is 8080.
The probability is conditional on the employee being a developer, which restricts the denominator of the probability to the total number of developers.
2
Identify the favorable outcomes within the subgroup.
There are 5050 developers whose primary operating system is Windows.
This value represents the numerator for our conditional probability calculation.
3
Calculate the conditional probability.
The probability is 5080=58\frac{50}{80} = \frac{5}{8} (or 0.6250.625).
Dividing the favorable outcomes by the total outcomes in the restricted sample space gives the correct conditional probability.

Key Concept

Conditional Probability in Two-Way Tables
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