# A box has cards numbered 114 to 199. cards are mixed throughly and a card is drawn from the bag at random. Find the probability that the number on the card, drawn from the box is (i) an odd no.(ii) a perfect square.

$Totalno.ofcards=199-114+1=85+1=86\phantom{\rule{0ex}{0ex}}no.ofoddcards=\frac{86}{2}=43\phantom{\rule{0ex}{0ex}}Probabilityofdrawinganoddcards=\frac{no.ofoddcards}{Totalno.ofcards}=\frac{42}{86}=\frac{21}{43}\phantom{\rule{0ex}{0ex}}perfectsquareswhichliesbetween199and114are144,169,and196\phantom{\rule{0ex}{0ex}}no.ofperfectsquares=3\phantom{\rule{0ex}{0ex}}Probabilityofdrawinganperfectsquares=\frac{no.ofperfectsquares}{Totalno.ofcards}=\frac{3}{86}$

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