For a particular species of wolf, 52% are female, 20% hunt in medium-sized packs

Question

For a particular species of wolf, 52% are female, 20% hunt in medium-sized packs, and 15% are both female and hunt in medium-sized packs.

Please explain each step and show venn diagrams if possible

(a) What is the proportion of wolves that are female but do not hunt in medium-sized packs?    

(b) What is the proportion of wolves that are neither female nor hunt in medium-sized packs?

(c) What is the proportion of wolves that are female but do not hunt in medium-sized packs or that are not female but hunt in medium-sized packs?   

(d) What is the probability of selecting a wolf that is female, given that it hunts in a medium-sized pack?

Explanation / Answer

probabilty of women =P(W)=0.52 and that of men =P(M)=0.42

probabilty of hunting in medim size packs =P(HM)=0.20

and P(W &HM)=0.15

a) proportion of wolves that are female but do not hunt in medium-sized packs=P(W&HMc)=P(W)-P(W&HM)

=0.52-0.15=0.37

b)proportion of wolves that are neither female nor hunt in medium-sized packs =P(M &MHc)=P(MHc)-P(W&MHc)

=0.8-0.37=0.43

c)proportion of wolves that are female but do not hunt in medium-sized packs or that are not female but hunt in medium-sized packs =P(W &MHc)+P(M &MH)=0.37+P(M)-P(M&MHc)=0.37+0.48-0.43=0.42

d) probability of selecting a wolf that is female, given that it hunts in a medium-sized pack=P(W|MH)

=P(W&MH)/P(MH)=0.15/0.2=0.75

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