A 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 2053
class attendees. The data is summarized in the table below.
Class Type and Member Status of Class Attendees
Class Type Member Non-Member
Barre 194
94
Boot Camp 210
279
Boxing 290
231
Spinning 276
286
Yoga 95
98
What is the probability that a class attendee is a member of the gym and is attending a barre class or is a non-member of the gym and is attending a boxing class? Enter a fraction or round your answer to 4
decimal places, if necessary.
First, we need to calculate the total number of class attendees for each category: member and non-member.
Total member attendees = 194 + 210 + 290 + 276 + 95 = 1065
Total non-member attendees = 94 + 279 + 231 + 286 + 98 = 988
Now, we find the probability of a class attendee being a member and attending a barre class:
P(member and barre) = 194/2053
Next, we find the probability of a class attendee being a non-member and attending a boxing class:
P(non-member and boxing) = 231/2053
Finally, we add these two probabilities together to get the probability that a class attendee is a member of the gym and attending a barre class or is a non-member of the gym and attending a boxing class:
P = P(member and barre) + P(non-member and boxing)
P = 194/2053 + 231/2053
P = 425/2053
Therefore, the probability that a class attendee is a member of the gym and is attending a barre class or is a non-member of the gym and is attending a boxing class is 425/2053, which is approximately 0.2071 or 0.2072 rounded to 4 decimal places.