Question

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 1

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

---

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

---

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

---

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

---

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

---

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