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kirill115 [55]
3 years ago
15

In its monthly report, the local animal shelter states that it currently has 24 dogs and 18 cats available for adoption. Eight o

f the dogs and 6 of the cats are male. Find each of the following conditional probabilities if an animal is selected at random: a) The pet is male, given that it is cat. b) The pet is a cat, given that it is female. c) The pet is female, given that it is a dog.
Mathematics
1 answer:
andrezito [222]3 years ago
5 0

Answer with Step-by-step explanation:

We are given that

Total dogs=24

Total cats=18

Total animals=24+18=42

Male dogs=8

Male cats=6

Total male animals=8+6=14

Total female animals=42-14=28

Female cats=18-6=12

Dogs female=24-8=16

a.We have to find the probability that the pet is male, given that it is cat.

It means we have to find P(Male/cat)  

Conditional probability: P(A/B)=\frac{P(A\cap B)}{P(B)}

P(Cat)=\frac{18}{42}

P(male cat)=\frac{6}{42}

P(Male/cat)=\frac{\frac{6}{42}}{\frac{18}{42}}

P(male/cat)=\frac{6}{18}=0.33

b.P(female cat)=\frac{12}{42}

P(female)=\frac{28}{42}

P(Cat/Female)=\frac{\frac{12}{42}}{\frac{28}{42}}=\frac{12}{28}=0.43

c.P(Dog)=\frac{24}{42}

P(dog female)=\frac{16}{42}

P(female/dog)=\frac{\frac{16}{42}}{\frac{24}{42}}

P(female/dog)=\frac{16}{24}=0.67

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