Question 1203255: In a group of 100 people, 40 own a cat, 25 own a dog and 15 own a cat and a dog. Find the probability that the person chosen at random
owns a dog or a cat,
owns a dog or a cat, but not both,
owns a dog, given that he owns a cat,
does not own a cat, given that he owns a dog.
Answer by ikleyn(52824)   (Show Source):
You can put this solution on YOUR website! .
In a group of 100 people, 40 own a cat, 25 own a dog and 15 own a cat and a dog.
Find the probability that the person chosen at random
(a) owns a dog or a cat,
(b) owns a dog or a cat, but not both,
(c) owns a dog, given that he owns a cat,
(d) does not own a cat, given that he owns a dog.
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The preliminary analysis:
(1) own a dog or a cat 40 + 25 - 15 = 50.
(2) own a dog or a cat, but not both: subtract 15 (that own both) from 50 (that own dog or cat; see (1) )
50-15 = 35.
Therefore, the answers for (a) and (b) are
question (a) P =  =  = 0.5 = 50%. ANSWER
question (b) P =  =  = 0.35 = 35%. ANSWER
(c) In the set of owing a cat, you are looking for the part owing a cat.
The probability is P =  =  =  = 0.3 = 30%. ANSWER
(d) From the set "own a dog", subtract the subset "own both" 25-15 = 10.
The probability is P =  =  = 0.4 = 40%. ANSWER
Solved.
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