Question 1203255
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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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<pre>
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 = {{{50/100}}} = {{{1/2}}} = 0.5 = 50%.     <U>ANSWER</U>

     question (b)  P = {{{35/100}}} = {{{7/20}}} = 0.35 = 35%.   <U>ANSWER</U>



(c)  In the set of owing a cat, you are looking for the part owing a cat.

     The probability is  P = {{{both/50}}} = {{{15/50}}} = {{{3/10}}} = 0.3 = 30%.    <U>ANSWER</U>



(d)  From the set "own a dog", subtract the subset "own both"  25-15 = 10.

     The probability is  P = {{{10/25}}} = {{{2/5}}} = 0.4 = 40%.    <U>ANSWER</U>
</pre>

Solved.