One card is drawn from a well-shuffled deck of 52 cards. Now, answer t

1.	One card is drawn from a well-shuffled deck of 52 cards. Now, answer the following questions: a). The probability of getting a king of red suit is : (i). \(\frac{1}{52}\)(ii). \(\frac{1}{26}\)(iii). \(\frac{1}{13}\)(iv). None. b). The probability of not getting a king of red suit is : (i). \(\frac{1}{26}\)(ii). \(\frac{25}{26}\)(iii).\(\frac{24}{26}\)(iv). None.c). The probability of getting a face card is : (i). \(\frac{1}{13}\)(ii). \(\frac{2}{13}\)(iii). \(\frac{3}{13}\)(iv). None. d). The probability of getting a red face card is : (i). \(\frac{1}{26}\)(ii). \(\frac{3}{26}\)(iii).\(\frac{15}{26}\)(iv). None. e). The probability of getting a spade is : (i). \(\frac{1}{2}\)(ii). \(\frac{1}{4}\)(iii). \(\frac{1}{13}\)(iv). None.
Answer» Total number of cars in the deck = 52. (a) Total king cards are 4 in which 2 are black suited and 2 are red suited. Therefore, total number of king card which is red suited = 2. Probability of getting a king of red suit = \(\frac{Total\, red\, suited\, king\,card}{Total\, number\, of\,cards\, in \,the\, deck}\) = \(\frac{2}{52} = \frac{1}{26}\) Hence, option (ii) is correct. (b) The probability of not getting a king or red suit = 1 – probability of getting a king of red suit = 1– \(\frac{1}{26}\) = \(\frac{25}{26}\) . Hence, option (ii) is correct. (c) Total number of face cards = 3 × 4 = 12. (∵ Jack, Queen & king cards are face cards) Therefore, the probability of getting a face and = \(\frac{Total\, number\, of\, face\, card}{Total\, number\, of\, cards\, in\, the \, deck}\) = \(\frac{12}{52}= \frac{3}{13}.\) Hence, option (iii) is correct. (d) Total number of red face card = 3× 2 = 6. Therefore, the probability of getting a red face card = \(\frac{Total\, number\, of\, red\, face\, card} {Total\, number\, of \,cards \,in \,deck}\) = \(\frac{6}{52} = \frac{3}{26}\) Hence, option (ii) is correct. (e) Total number of spade cards = 13. Therefore, the probability of getting a spade card = \(\frac{Total \,number\,of \,spade \,cards}{Total \,number\, of \,cards\, in \,the\, deck}\) = \(\frac{13}{52} = \frac{1}{4}\)

One card is drawn from a well-shuffled deck of 52 cards. Now, answer the following questions: a). The probability of getting a king of red suit is : (i). \(\frac{1}{52}\)(ii). \(\frac{1}{26}\)(iii). \(\frac{1}{13}\)(iv). None. b). The probability of not getting a king of red suit is : (i). \(\frac{1}{26}\)(ii). \(\frac{25}{26}\)(iii).\(\frac{24}{26}\)(iv). None.c). The probability of getting a face card is : (i). \(\frac{1}{13}\)(ii). \(\frac{2}{13}\)(iii). \(\frac{3}{13}\)(iv). None. d). The probability of getting a red face card is : (i). \(\frac{1}{26}\)(ii). \(\frac{3}{26}\)(iii).\(\frac{15}{26}\)(iv). None. e). The probability of getting a spade is : (i). \(\frac{1}{2}\)(ii). \(\frac{1}{4}\)(iii). \(\frac{1}{13}\)(iv). None.

Answer»

Total number of cars in the deck = 52.

(a) Total king cards are 4 in which 2 are black suited and 2 are red suited.

Therefore, total number of king card which is red suited = 2.

Probability of getting a king of red suit

= \(\frac{Total\, red\, suited\, king\,card}{Total\, number\, of\,cards\, in \,the\, deck}\) = \(\frac{2}{52} = \frac{1}{26}\)

Hence, option (ii) is correct.

(b) The probability of not getting a king or red suit = 1 – probability of getting a king of red suit

= 1– \(\frac{1}{26}\) = \(\frac{25}{26}\) .

Hence, option (ii) is correct.

(c) Total number of face cards = 3 × 4 = 12. (∵ Jack, Queen & king cards are face cards)

Therefore, the probability of getting a face and

= \(\frac{Total\, number\, of\, face\, card}{Total\, number\, of\, cards\, in\, the \, deck}\) = \(\frac{12}{52}= \frac{3}{13}.\)

Hence, option (iii) is correct.

(d) Total number of red face card = 3× 2 = 6.

Therefore, the probability of getting a red face card

= \(\frac{Total\, number\, of\, red\, face\, card} {Total\, number\, of \,cards \,in \,deck}\) = \(\frac{6}{52} = \frac{3}{26}\)

Hence, option (ii) is correct.

(e) Total number of spade cards = 13.

Therefore, the probability of getting a spade card

= \(\frac{Total \,number\,of \,spade \,cards}{Total \,number\, of \,cards\, in \,the\, deck}\) = \(\frac{13}{52} = \frac{1}{4}\)

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