From pack of 52 playing cards, blackjacks, black kings and black aces.

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From pack of 52 playing cards, blackjacks, 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.

Solution:

Total number of cards = 52
Black jacks, black kings and black aces are removed
Now number of cards = 52 – (2 + 2 + 2) = 52 – 6 = 46
One card is drawn
(i) No. of red cards = 13 + 13 = 26
∴Probability = \\ \frac { 26 }{ 46 } = \\ \frac { 13 }{ 23 }
(ii) Face cards = 4 queens, 2 red jacks, 2 kings = 8
∴Probability = \\ \frac { 8 }{ 46 } = \\ \frac { 4 }{ 23 }
(iii) a diamond on a club = 13 + 10 = 23
∴Probability = \\ \frac { 23 }{ 46 } = \\ \frac { 1 }{ 2 }
(iv) A queen or a spade = 4 + 10 = 14
∴Probability = \\ \frac { 14 }{ 46 } = \\ \frac { 7 }{ 23 }

Two dice are thrown together. Find the probability that the product of the numbers on the top of two dice is
(i) 6
(ii) 12
(iii) 7

Solution:

Two dice are thrown together
Total number of events = 6 × 6 = 36
(i) Product 6 = (1, 6), (2, 3), (3, 2). (6, 1) = 4
Probability = \\ \frac { 4 }{ 36 } = \\ \frac { 1 }{ 9 }
(ii) Product 12 = (2, 6), (3, 4), (4, 3), (6, 2) = 4
Probability = \\ \frac { 4 }{ 36 } = \\ \frac { 1 }{ 9 }
(iii) Product 7 = 0 (no outcomes)
Probability = \\ \frac { 0 }{ 36 } = 0

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