There are 52 cards in a deck of playing cards. If a card is drawn from this well shuffled deck, the total number of all possible outcomes = 52.
(i) Let the event of drawing a red king be R.
Since a deck has four kings in it out of which 2 kings are red.
∴ The number of favourable outcomes of getting a red king.
Let the probability of this event be R =2.
∴ P(R)
= \(\frac { 2 }{ 52 }\) = \(\frac { 1 }{ 26 }\)
(ii) Let the event according a face card be (E)
∵ Since each of the group of has 3 face cards (king, queen, and jack) in it.
∴ Number of face cards in the deck
= 3 × 4 = 12
∴ The probability of event (E) = P(E)
= \(\frac { 12 }{ 52 }\) = \(\frac { 3 }{ 13 }\)
(iii) Let the event of a red face card be (A)
∵ N number of face cards in the deck = 12
∴ Number of red face cards in the deck = 6
Then the number of possible outcomes of event (A).
⇒ P(A)
= \(\frac { 6 }{ 52 }\) = \(\frac { 3 }{ 26 }\)
(iv) Let the event of hearts jack be (B).
∵ There is only one hearts jack in the deck.
So the number of favourable outcomes of (B) = 1
∴ The probability of event (B)
⇒ P(B)
= \(\frac { 1 }{ 52 }\)
(v) Let the event occurring a spades card be (C).
∵ The number of spades cards in the deck 13.
∴ The number of favourable outcomes of event (C) = 13.
The probability of event (C) = \(\frac { 13 }{ 52 }\).
⇒ P(C) = \(\frac { 1 }{ 4 }\)
(vi) Let the event occurring a diamonds queen be (D).
∵ There is only one diamonds queen in the deck.
∴ The number of favourable outcomes of event (D) = 1
The probability of (D)
⇒ P(D) = \(\frac { 1 }{ 52 }\)
