Question

question
135 physical therapists were asked if they use their complimentary gym membership and if
they bring their own lunch to work.
the following table shows the results.

according to the table, what is the probability that a randomly chosen physical therapist does
not use the gym membership given that they bring their lunch to work? give your answer as a
fraction in simplest form.

provide your answer below:

Explanation:

Step1: Recall Conditional Probability Formula

The formula for conditional probability is \( P(A|B) = \frac{P(A \cap B)}{P(B)} \). In the context of a contingency table, this translates to \( P(\text{Does Not Use Gym} | \text{Brings Lunch}) = \frac{\text{Number of therapists who do not use gym and bring lunch}}{\text{Number of therapists who bring lunch}} \).

Step2: Identify the Values from the Table

From the table, the number of therapists who do not use the gym membership and bring lunch to work is 18. The number of therapists who bring lunch to work is 42.

Step3: Calculate the Probability

Substitute the values into the formula: \( \frac{18}{42} \). Simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 6. \( \frac{18 \div 6}{42 \div 6} = \frac{3}{7} \).

Answer:

\(\frac{3}{7}\)