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

i) King of red colour can be hearts King or a diamond king.

So, the possibility is $2.$

$P($Red king$)=\frac{2}{52}=\frac{1}{26}$

ii) A face card can be jack, queen, king of any suite.

In this way we will get $3\times 4=12$ face cards.

$P($Face card$)=\frac{12}{52}=\frac{3}{13}$

iii) A red face card can be either hearts or diamond king, jack or queen, which means there are $3\times 2=6$

$P($Red face card$)=\frac{6}{52}=\frac{3}{26}$

iv) There is only one Jack of hearts.

$P($Jack of hearts$)=\frac{1}{52}$

v) There are $13$ spades in total.

So, $P($Spade$)=\frac{13}{52}=\frac{1}{4}$

vi) There is only one queen diamond.

Hence, $P($Queen diamond$)=\frac{1}{52}$