Question

One card is drawn from a well – shuffled deck of 52 cards. Find the probability of getting
$\begin{array}{cc}\text{(i) a king of red colour}& \text{(ii) a face card}\\ \text{(iii) a red face card}& \text{(iv) the jack of hearts}\\ \text{(v) a spade}& \text{(vi) the queen of diamonds}\end{array}$

Answer 1

Out of 52 cards, one card can be drawn in 52 ways. So, total number of elementary events = 52

(i) There are two suits of red cards viz. diamond and heart. Each suit contains one king.

Therefore, Favourable number of elementary events $=2\times 1=2$

Hence, P(a king of red colour) $=\frac{2}{52}=\frac{1}{26}$

(ii) In a deck of 52 cards: kings, queens and jacks are called face cards. Thus, there are 12 face cards. So, one face card can be chosen in 12 ways. Therefore, Favourable number of elementary events = 12

Hence, P(a face card) $=\frac{12}{52}=\frac{3}{13}$

(iii) There are two suits of red cards viz. diamond and heart. Each suit contains 3 facecards.

Therefore, Favourable number of elementary events $=2\times 3=6$

Hence, P(a red face card) $=\frac{6}{52}=\frac{3}{26}$

(iv)There is only one jack of hearts

Therefore, Favourable number of elementary events = 1

Hence, P(the jack of hearts) $=\frac{1}{52}$

(v) There are 13 cards of spade.

Therefore, Favourable number of elementary events = 13

Hence, P(a spade) $=\frac{13}{52}=\frac{1}{4}$

(vi) There is only one queen of diamonds.

Therefore, Favourable number of elementary events = 1

Hence, P(the queen of diamonds) $=\frac{1}{52}$.