SOLUTION: 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, ï

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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(52834)   (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.
~~~~~~~~~~~~~~~~~~~~~~~ 

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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