Question

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 therewere 2317 class attendees. The data is summarized in the table below.Class Type and Member Status of ClassAttendeesClass TypeMemberNon-MemberBarreBoot CampBoxingSpinningYoga29025420795232241245169297287What is the probability that a class attendee is a non-member of the gym and is attending a barre class or is a member of the gym and is attending a yoga class? Enter afraction or round your answer to 4 decimal places, if necessary. Lo

Answer 1

First, the probability of a class attendee being a non-member and attending a barre class is

`P(Non\cap Barre)=(241)/(2317)`

While the probability of class attendee being a member and attending a yoga class is

`P(Member\cap Yoga)=(232)/(2317)`

Finally, the probability of the first event or the second event is

`\begin{gathered} P((Non\cap Barre)\cup(Member\cap Yoga))=P(Non\cap Barre)+P(Member\cap Yoga) \\ =(232+241)/(2317)=(473)/(2317) \end{gathered}`

In a decimal expression,

`\Rightarrow P((Non\cap Barre)\cup(Member\cap Yoga))=0.204143\ldots\approx0.2041`

The answer is 473/2