Question

If 2 black kings and 2 red aces are removed from a deck of 52 cards, find the probability of getting

(i)    ati ace of heart
(ii)    a king
(iii)    a ace
(iv)    a heart
(v)    a red card

Solution

If 2 black kings and 2 red aces are removed from a deck of 52 cards, then possible outcomes are 52 – 4 = 48
i.e. n (S) = 48
(i) Let E be the favourable outcomes of getting an ace, then
n(E) = 0
Therefore,
P(E) = $fraction numerator straight n left parenthesis straight E right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 0 over 48 equals 0$

(ii) Let F be the favourable outcomes of getting an ace, then
n(F) = 2
Therefore,
P(F) = $fraction numerator straight n left parenthesis straight F right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 2 over 48 equals 1 over 24$

(iii) Let G be the favourable outcomes of getting a king, then
n(G) = 2
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 2 over 48 equals 1 fourth

(iv) Let H be the favourable outcomes of getting a heart, then H = {Total red cards - one red card which is removed) i.e., n (H) = 12 Therefore,
p(H) =

fraction numerator straight n left parenthesis straight H right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 12 over 48 equals 1 fourth

(v) Let 1 be the favourable outcomes of getting a red card, then,
n(I) = 24
Therefore,
P(I) = $fraction numerator straight n left parenthesis straight I right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 24 over 48 equals 1 half$

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Real Numbers

If 2 black kings and 2 red aces are removed from a deck of 52 cards, find the probability of getting

(i)    ati ace of heart
(ii)    a king
(iii)    a ace
(iv)    a heart
(v)    a red card

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The sum of the probabilities of all the elemen-tary events of an experiment is ______.

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