# One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that the card will be (i) diamond (ii) not an ace (iii) a black card.

Dear Student,

$Given:Awellshufleddeckof52cardsinwhicheachoutcomeisequallylikelyandonecardisdrawnfromit.\phantom{\rule{0ex}{0ex}}ToCalculate:Probabilitythatthedrawncardwillbe\left(a\right)diamond\left(b\right)Notanace\left(c\right)ablackcard\phantom{\rule{0ex}{0ex}}\left(a\right)thereare13diamondsinadeck\phantom{\rule{0ex}{0ex}}\Rightarrow Probabilitythatthedrawncardwillbediamond=\frac{13}{52}=\frac{1}{4}\phantom{\rule{0ex}{0ex}}\left(b\right)thereare4acesinadeckonefromeachsuit\phantom{\rule{0ex}{0ex}}So,no.ofcardthatarenotace=52-4=48\phantom{\rule{0ex}{0ex}}\Rightarrow Probabilitythatthedrawncardwillnotbeanace=\frac{48}{52}=\frac{12}{13}\phantom{\rule{0ex}{0ex}}\left(a\right)thereare26blackcardsinadeck\phantom{\rule{0ex}{0ex}}\Rightarrow Probabilitythatthedrawncardwillbeablackcard=\frac{26}{52}=\frac{1}{2}$

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