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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

Solution:

i) King of red colour can be hearts King or a diamond king. So, the possibility is 2.
P(Red king) = 2/52 = 1/26
ii) A face card can be jack, queen, king of any suite. In this way we will get 3 × 4 = 12 face cards.
P(Face card) = 12/52 = 3/13
iii) A red face card can be either hearts or diamond king, jack or queen, which means there are 3 × 2 = 6
P(Red face card) = 6/52 = 3/26
iv) There is only one Jack of hearts.
P(Jack of hearts) = 1/52
v) There are 13 spades in total. So,
P(Spade) = 13/52 = 1/4
vi) There is only one queen diamond. Hence,
P(Queen diamond) = 1/52