Question

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is:
(i) a black king
(ii) either a black card or a king
(iii) black and a king
(iv) a jack, queen or a king
(v) neither a heart nor a king
(vi) spade or an ace
(vii) neither an ace nor a king
(viii) neither a red card nor a queen.
(ix) other than an ace
(x) a ten
(xi) a spade
(xii) a black card
(xiii) the seven of clubs
(xiv) jack
(xv) the ace of spades
(xvi) a queen
(xvii) a heart
(xviii) a red card

Answer 1

(i) There are two black kings, spade and clover. Hence, the probability that the drawn card is a black king is: 2/52 = 1/26
(ii) There are 26 black cards and 4 kings, but two kings are already black. Hence, we only need to count the red kings. Thus, the probability is: (26+2)/52 = 7/13
(iii) This question is exactly the same as part (i). Hence, the probability is: 2/52 = 1/26
(iv) There are 4 jacks, 4 queens and 4 kings in a deck. Hence, the probability of drawing either of them is: (4+4+4)/52 = 3/13
(v) This means that we have to leave the hearts and the kings out. There are 13 hearts and 3 kings (other than that of hearts). Hence, the probability of drawing neither a heart nor a king is: (52-13-3)/52 = 9/13
(vi) There are 13 spades and 3 aces (other than that of spades). Hence the probability is: (13+3)/52 = 4/13
(vii) This means that we have to leave the aces and the kings out. There are 4 aces and 4 kings. Hence, the probability of drawing neither an ace nor a king is: (52$-$4$-$4)/52 = 11/13.
(viii) This means that we have to leave the red cards and the queens out. There are 26 red cards and 2 queens (only black queens are counted since the reds are already counted among the red cards). Hence, the probability of drawing neither a red card nor a queen is: (52-26-2)/52 = 6/13
(ix) It means that we have to leave out the aces. Since there are 4 aces, then the probability is (52$-$4)/52 = 12/13
(x) Since there are four 10s, the probability is: 4/52 = 1/13
(xi) Since there are 13 spades, the probability is: 13/52 = 1/4
(xii) Since there are 26 black cards, the probability is: 26/52 = 1/2
(xiii) There is only one card named seven of clubs. Hence, the probability is 1/52.
(xiv) Since there are 4 jacks, the probability is: 4/52 = 1/13
(xv) There is only 1 card named ace of spade. Hence, the probability is 1/52.
(xvi) Since there are 4 queens, the probability is: 4/52 = 1/13
(xvii) Since there are 13 hearts, the probability is: 13/52 = 1/4
(xviii) Since there are 26 red cards, the probability is 26/52 = 1/2