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Mathematics Question on Probability

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting
(i) a king of red colour
(ii) a face card
(iii) a red face card
(iv) the jack of hearts
(v) a spade
(vi) the queen of diamonds

Answer

Total number of cards in a well-shuffled deck = 52
(i) Total number of kings of red colour = 2
Probability of getting a king of red colour=Number  of favourable  outcomesNumber  of  total  possible outcomes\text{Probability of getting \bf{a king of red colour}}=\frac{\text{Number}\ \text{ of} \ \text{favourable}\ \text{ outcomes}}{\text{Number}\ \text{ of }\ \text{total }\ \text{possible} \ \text{outcomes}}
=252=126=\frac{2}{52}=\frac{1}{26}

(ii) Total number of face cards = 12
Probability  of  getting a face card=Number  of favourable  outcomesNumber  of  total  possible outcomes\text{Probability}\ \text{ of}\ \text{ getting} \,\bf{ a\, face \,card} =\frac{\text{Number}\ \text{ of} \ \text{favourable}\ \text{ outcomes}}{\text{Number}\ \text{ of }\ \text{total }\ \text{possible} \ \text{outcomes}}
=1252=313=\frac{12}{52}=\frac{3}{13}

(iii) Total number of red face cards = 6
Probability  of  getting  a  red face card =Number  of favourable  outcomesNumber  of  total  possible outcomes\text{Probability}\ \text{ of}\ \text{ getting}\ \textbf{ a \,red\,face\,card}\ =\frac{\text{Number}\ \text{ of} \ \text{favourable}\ \text{ outcomes}}{\text{Number}\ \text{ of }\ \text{total }\ \text{possible} \ \text{outcomes}}
=652=326=\frac{6}{52}=\frac{3}{26}

(iv) Total number of Jack of hearts = 1
Probability  of  getting  a jack of hearts=Number  of favourable  outcomesNumber  of  total  possible outcomes\text{Probability}\ \text{ of}\ \text{ getting}\ \textbf{ a jack of hearts}=\frac{\text{Number}\ \text{ of} \ \text{favourable}\ \text{ outcomes}}{\text{Number}\ \text{ of }\ \text{total }\ \text{possible} \ \text{outcomes}}
=152=\frac{1}{52}

(v) Total number of spade cards = 13
Probability  of  getting  a spade  card=Number  of favourable  outcomesNumber  of  total  possible outcomes\text{Probability}\ \text{ of}\ \text{ getting}\ \textbf{ a spade\, card} =\frac{\text{Number}\ \text{ of} \ \text{favourable}\ \text{ outcomes}}{\text{Number}\ \text{ of }\ \text{total }\ \text{possible} \ \text{outcomes}}
=1352=14=\frac{13}{52}=\frac{1}{4}

(vi) Total number of queen of diamonds = 1
Probability  of  getting  a queen of diamond=Number  of favourable  outcomesNumber  of  total  possible outcomes\text{Probability}\ \text{ of}\ \text{ getting}\ \textbf{ a queen of diamond}=\frac{\text{Number}\ \text{ of} \ \text{favourable}\ \text{ outcomes}}{\text{Number}\ \text{ of }\ \text{total }\ \text{possible} \ \text{outcomes}}
=152=\frac{1}{52}