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One card is drawn from a pack of 52 cards, each of the 52 cards being equal likely to be drawn. Find the probability that the card drawn is (i) An ace, (ii) red, (iii) either red or king, (iv) red and a king, (v) a face card, (vi) a red face card, (vii) ‘2’ of spade, (viii) ’10’ of a blacksuit.

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n(S) = 52

(i)  Event = {an ace}

n (E) = 4

P (E) =?

∴ P (E) = n (E)/n (S) = 4/52 = 1/13.

(ii) Event = {red cards}

n(E) = 26

P (E) =?

∴ P (E) = n (E)/n (S) = 26/52 = ½.

(iii) Event = {either red or king}

= {26 red cards + 2 kings}

= 28

n (E) = 28

P (E) =?

∴ P (E) = n (E)/n (S) = 28/52 =7/13.

(iv)  Event = {red and a king}

= (there are 2 red kings in a pack of 52 cards}.

n (E) = 2

P (E) =?

∴ P (E) = n (E)/n (S) = 2/52 = 1/26.

(v) Event = {face cards}

n (E) = 2

P (E) =?

∴ P (E) = n (E)/n (S) = 12/52 = 3/13.

(vi) Event = {red face cards} = {3 diamonds + 3 hearts}

n (E) = 6

P (E) =?

∴ P (E) = n (E)/n (S) = 6/52 = 3/26.

(vii) Event = {‘2’ of grade}

n (E) = 1

P (E) =?

∴ P (E) = n (E)/n (S) = 1/52.

(viii) Event = {‘10’ of blacksuit}

n (E) = 2

P (E) =?

∴ P (E) = n (E)/n (S) = 2/52 = 1/26.

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