AM i correct with these answers Participantsmillions Activit

?AM i correct with these answers?

Participants(millions)

Activity

Male

Female

Bicycle riding

22.2

21.0

Camping

25.6

24.3

Exercise walking

28.7

57.7

Exercising with equipment

20.4

24.4

Swimming

26.4

34.4

0.164576803      =21/127.6         Bicycle riding

0.190438871      =24.3/127.6       Camping

0.452194357      =57.7/127.6       Exercise walking

0.191222571      =24.4/127.6       Exercising with equipment

0.269592476      =34.4/127.6       Swimming

0.183622829      =22.2/120.9       Bicycle riding

0.211745244      =25.6/120.9       Camping

0.23738627        =28.7/120.9       Exercise walking

0.168734491      =20.4/120.9       Exercising with equipment

0.218362283      =26.4/120.9       Swimming

0.347686117      =(28.7+57.7)/248.5

=28.7/1209        0.23738627        Probability Exercise Walker is a Male

=57.7/127.6       0.452194357      Probability Exercise Walker is a Female

Solution

Other than last part, every thing else is correct. In the last part when we happen to see an exercise walker going by the probabilities are as follows:

P(male exercise  walker) = 28.7/(28.7+57.7) = 0.33217

P(female exercise  walker) = 57.7/(28.7+57.7)=0.66782

Explanation: When we have observed that the activity is exercise walking, then immediately our domain of interest shrinks down only to the total people with exercise walking. We are no longer interested in any other activity whatsoever, because there is certainty that the activity is exercise walking.

Now we just have to find that the person observed walking was male or female.

So, P(<male/female> walker) = (number of <male/female> walkers) / (total number of walkers {= 28.7+57.7=86.4 })

Also, you can also verify your answer by checking whether sum of probabilities = 1, if all the cases are covered. Here since the walker could only be male or female, so sum of probabilities considering both possible cases of male and female should add upto 1.