From pack of 52 playing cards, black jacks, black kings and black aces are removed and then the remaining pack is well-shuffled. A card is drawn at random from the remaining pack. Find the probability of getting

(i) a red card

(ii) a face card

(iii) a diamond or a club

(iv) a queen or a spade.

There are 2 black jacks, 2 black kings and 2 black aces.

No. of cards left after removing black jacks, black kings and black aces = 52 - 6 = 46.

(i) There are 26 red cards, 13 of hearts and 13 of diamonds.

∴ P(a red card) = $\dfrac{26}{46} = \dfrac{13}{23}.$

Hence, the probability of drawing a red card = $\dfrac{13}{23}.$

(ii) There are 12 face cards, out of which 4 are removed.

No. of face cards left = 8,

P(a face card) = $\dfrac{8}{46} = \dfrac{4}{23}.$

Hence, the probability of drawing a face card = $\dfrac{4}{23}.$

(iii) There are 13 cards in diamond and 13 cards in club.

Out of club, one king, one queen and one ace is removed,

No. of club cards left = 13 - 3 = 10.

Total no. of diamond and club cards = 13 + 10 = 23.

P(a diamond or club) = $\dfrac{23}{46} = \dfrac{1}{2}.$

Hence, the probability of drawing a diamond or club card = $\dfrac{1}{2}.$

(iv) There are 13 cards in spade and 4 queens (including the queen of spade).

Out of spade, one king, one queen and one ace is removed,

No. of spade cards left = 13 - 3 = 10.

3 queens are left after removing the queen of spade, as it is already included while counting spade cards.

Total no. of spade and queens = 10 + 3 = 13.

P(a spade or queen) = $\dfrac{13}{46}.$

Hence, the probability of drawing a spade or queen = $\dfrac{13}{46}.$