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Real Numbers

Question
CBSEENMA10009377
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A card is drawn from a pack of 52 playing cards. What is the probability that it is

(i) an ace
(ii)    a face card
(iii)    any card numbered from 2 to 10?

Solution

Total number of all possible outcomes = 52
i.e., n( S) = 52
(i) Let E be the favourable outcomes of getting an ace, then
n(E) = 4 Therefore,
P(E) = fraction numerator straight n left parenthesis straight E right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 4 over 52 equals 1 over 13.

(ii) Let F be the favourable outcomes of getting a face card, then
n(F) = 12 Therefore,
P(F) = fraction numerator straight n left parenthesis straight F right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 12 over 52 equals 3 over 13

(iii) Let G be the favourable outcomes of getting any card numbered from 2 to 10, then n(G)= {36}

Therefore,
P(G) = fraction numerator straight n left parenthesis straight G right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 36 over 52 equals 9 over 13.

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