Use the following information for questions (20) - (22). 50% of people in a grou

Question

Use the following information for questions (20) - (22). 50% of people in a group own a dog. 40% own a cat, and 20% own both. Given that a person owns a cat, what is the probability they own a dog? (a) 72% (b) 50% (c) 12% (d) 33% If you choose 3 people at random from this sample, what is the probability that all 3 own a cat? Assume independence between people. (a) 0.015 (b) 0.064 (c) 0.129 (d) 0.322 Are the outcomes "owning a dog" and "owning a cat" independent? (a) Yes (b) No (c) Not enough information.

Explanation / Answer

P(A) DOG = 50%

P(B) CAT = 40%

P(A AND B) =20%

A)   Prob( A and B)/Prob(b) =   

prob(dog | cat) = prob(dog and cat)/prob(cat)   20% /40% = 0.5 = 50%

B) total number of people chosen three randomly=0.9c3

out of 40 cats three are chosen = 0.4c3

probabilty= 0.4c3/0.9c3=0.064

22)

yes independent

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