A survey of employees at a company recorded their preferred vacation season and the...
Check the final answer first, then review the worked steps.
Problem
A survey of employees at a company recorded their preferred vacation season and their office location (California or New York). The data is presented in a table. The question asks for the conditional probability that a randomly selected employee prefers to go on vacation in winter, given that the employee works out of the company's New York offices.
Answer
\(3/10 or 0.3\)
Step-by-step solution
- Identify the relevant data: The problem asks for the probability that an employee prefers winter vacation GIVEN that they work in the New York office. This is a conditional probability problem.
- Determine the total number of employees in the New York office: Look at the 'New York' column in the table and sum the numbers for each season: $7 (\text{Spring}) + 9 (\text{Summer}) + 5 (\text{Autumn}) + 9 (\text{Winter}) = 30$ employees.
- Determine the number of employees in the New York office who prefer winter vacation: From the table, the number of employees in the New York office who prefer winter vacation is $9$.
4. Calculate the conditional probability: The probability of event A (preferring winter vacation) given event B (working in the New York office) is calculated as $P(A|B) = \frac{\text{Number of outcomes in both A and B}}{\text{Number of outcomes in B}}$.
In this case, A is preferring winter vacation, and B is working in the New York office.
So, the probability is $\frac{\text{Number of employees in New York who prefer winter}}{\text{Total number of employees in New York}} = \frac{9}{30}$.
5. Simplify the fraction: The fraction $\frac{9}{30}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
$\frac{9 \div 3}{30 \div 3} = \frac{3}{10}$.
- Convert to decimal (optional but requested): To express the answer as a decimal, divide the numerator by the denominator: $3 \div 10 = 0.3$.