Math  /  Data & Statistics

QuestionA group fitness gym classifies its fitness class attendees by class type and member status. The marketing team has gathered data from a random month, in which there were 2101 class attendees. The data is summarized in the table below. \begin{tabular}{|c|c|c|} \hline \multicolumn{3}{|c|}{ Class Type and Member Status of Class } \\ Attendees \\ \hline Class Type & Member & Non-Member \\ \hline Barre & 271 & 153 \\ \hline Boot Camp & 235 & 287 \\ \hline Boxing & 239 & 100 \\ \hline Spinning & 279 & 206 \\ \hline Yoga & 166 & 165 \\ \hline \end{tabular}
What is the probability that a class attendee is a non-member of the gym and is attending a boxing class or is a member of the gym and is attending a spinning class? Enter a fraction or round your answer to 4 decimal places, if necessary.

Studdy Solution

STEP 1

1. The total number of class attendees is 2101.
2. The classification of attendees is based on class type and member status.
3. We need to find the probability of either a non-member attending a boxing class or a member attending a spinning class.

STEP 2

1. Identify the total number of non-members attending a boxing class.
2. Identify the total number of members attending a spinning class.
3. Calculate the combined probability of the two disjoint events.
4. Express the probability as a fraction or a decimal rounded to 4 decimal places.

STEP 3

Identify the number of non-members attending a boxing class.
From the table, the number of non-members attending a boxing class is: 100 100

STEP 4

Identify the number of members attending a spinning class.
From the table, the number of members attending a spinning class is: 279 279

STEP 5

Calculate the combined number of attendees for the two disjoint events.
The total number of attendees in these categories is: 100+279=379 100 + 279 = 379

STEP 6

Calculate the probability of a class attendee being either a non-member attending a boxing class or a member attending a spinning class.
The probability is given by the ratio of the combined number of attendees to the total number of attendees: P=3792101 P = \frac{379}{2101}

STEP 7

Express the probability as a decimal rounded to 4 decimal places.
P37921010.1804 P \approx \frac{379}{2101} \approx 0.1804
Solution: The probability that a class attendee is a non-member of the gym and is attending a boxing class or is a member of the gym and is attending a spinning class is approximately: 37921010.1804 \frac{379}{2101} \approx 0.1804

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord