Given that a randomly chosen person lives in a house with a

Given that a randomly chosen person lives in a house with a backyard with probability of .4 and lives in a house with no backyard with a probability of 0.3, Moreover, a randomly chosen person lives in an apartment building with no backyard with a probability of 0.3.

Find the probability that a randomly chosen person does not have a backyard

Find the probability that a randomly chosen person lives in a house given that he does not have a backyard

Find the probability that a randomly chosen person lives in an apartment building with a backyard_____.

Solution

probability for living in a house and having a backyard = 0.4

and that for not having backyard = 0.3

probability that he lives in a apartment = 0.3

probability that a randomly chosen person does not have a backyard

= 0.3 + 0.3 = 0.6
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probability for not having a backyard = 0.3 + 0.3 = 0.6

out of which probability living in a house = 0.3

so required probability that a randomly chosen person lives in a house

provided that he does not have a backyard = 0.3/0.6 = 1/2 = 0.5

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the probability that a randomly chosen person lives in an apartment building

with a backyard is zero (0)

because no person living in apartment had a backyard.