Three of the most popular exhibits at the zoo are the lions, gorillas, and kanga

Question

Three of the most popular exhibits at the zoo are the lions, gorillas, and kangaroos. The number of unique guest that visit each exhibit was recorded: 20 guest visited the lions, 35 visited the gorillas, and 25 visited the kangaroos. Out of the guests that at each exhibit 14 guest took pictures with the lions, 20 with the gorillas, and 15 with the kangaroos. (a) What is the P(Visiting the lion)? P(Visiting the gorillas)? P(Visiting the kangaroos)? (b) What is the probability for each site of taking a picture with the animals? (c) What is the probability that someone visited the kangaroos given that they took a picture?

Explanation / Answer

a) Total guests is 20+35+25=80

P(visiting the lion)=20/80=0.25

P(visting the gorillas)=35/80=0.4375

P(visting the kangaroos)=25/80=0.3125

b) P(taking picture of lion given that one visiting lion)=14/20=0.7

P(taking picture of gorilla given that one visiting gorilla)=20/35=0.571

P(taking picture of kangaroo given that one visiting kangaroo)=15/25=0.6 or 60%

c) P(visiting kangaroo given that took picture)= P(taking picture of kangaroo given that one visiting kangaroo)*P(visiting kangaroo)/ (P(taking picture of lion given that one visiting lion)*P(visiting lion)+P(taking picture of gorilla given that one visiting gorilla)*P(visiting gorilla)+P(taking picture of kangaroo given that one visiting kangaroo)*P(visiting kangaroo))

=(0.6*0.3125)/(0.25*0.7+0.4375*0.571+0.6*0.3125)

=0.3062

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