Question

A 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) the queen of diamonds.

Answer 1

Total number of cards in a deck of cards = 52

∴Total number of outcomes = 52

(i) Let A denote the event of getting a king of red colour.

There are two cards in favour of getting a king of red colour i.e., King of heart and King of diamond.

Number of outcomes in favour of event A = 2

`thereforeP(A)=\text{Outcomes in favour of event A}/\text{Total number of outcomes}=2/25=1/26`

(ii) Let B denote the event of getting a face card.

There are 12 cards in favour of getting a face card i.e., 4 King, 4 Queen and 4 Jack cards.

Number of outcomes in favour of event B = 12

`thereforeP(B)=\text{Outcomes in favour of eventB}/\text{Total number of outcomes}=12/52=3/13`

(iii) Let C denote the event of getting a queen of diamond.

There is one queen of diamond in the deck of cards.

Number of outcomes in favour of event C = 1

`thereforeP(C)=\text{Outcomes in favour of eventC}/\text{Total number of outcomes}=1/52`