A card is drawn at random from a well-shuffled deck of playing cards. Find the probability of drawing a (i) face card (ii) Card which is neither a king nor a red card.

Solution

f one card is drawn from a well-shuffled deck of playing card, then possible outcome(s) are (52)
i.e., n(S) = 52
I. Let A be the favourable outcomes of getting a face card, then
i.e., n(A) = 12
Therefore,
$rightwards double arrow space straight P left parenthesis straight A right parenthesis space equals fraction numerator straight n left parenthesis straight A right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 12 over 52 equals 3 over 13$

II. Let B be the favourable outcomes of getting card which is neither a king nor a red card, then i.e., n(B) = 24

Therefore,

rightwards double arrow space space straight P left parenthesis straight B right parenthesis equals fraction numerator straight n left parenthesis straight B right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 24 over 52 equals 6 over 13

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Real Numbers

A card is drawn at random from a well-shuffled deck of playing cards. Find the probability of drawing a (i) face card (ii) Card which is neither a king nor a red card.

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