Question

Experiment: Selecting a single card from a standard playing deck. Which has 4 suits (Hearts, Clubs, Spades, and Diamonds) and 13 Cards per suit (2-10, Jack, Queen, King, Ace) . So there are a total of 52 cards.
Event A = Pulling an even number card (2,4,6,8,10)
Event B = Pulling a Diamond Card
Event C = Pulling a Face Card (Jack, Queen, King)
Calculate P(C)
Calculate P( C c )
Calculate P(A ∩ C c )
Calculate P(C ∩ A c )
Calculate P(C ∪ B c )
Calculate P(B ∪ C)
Calculate P(A | C c )
Calculate P(B | A c )

Answer 1

Probability for the following events will be :-

The probability of an event E,P(E)=

 Number of favourable outcomes / Total number of outcomes

​ =  n(E) / n(S)

​

Applying the concept of probability as shown above, let's calculate all the probabilities one by one.

(i) Probability of getting a king of red colour:

We know that, there are 26 red cards, 13 each of hearts and diamonds. Hence, there will be 1 king each in hearts and diamonds.

∴  Number of kings of red colour, n(E)=2

Also, total number of cards, n(S)=52

∴  Probability of getting a king of red colour

= n(E) / n(S)

= 2 / 52

⇒ 1 / 26

Hence, the required probability is  1 / 26

​(ii) Probability of getting a face card:

We know that, each suit has 3 face cards (Jack, Queen and King). Hence, there will be 12 face cards in total.

∴  Number of face cards, n(E)=12

Also, total number of cards, n(S)=52

∴  Probability of getting a face card

= n(E) / n(S)

= 12 / 52

⇒ 3 / 13

Hence, the required probability is  3 / 13

(iii) Probability of getting the jack of hearts:

We know that, there is only one jack in hearts.

∴  Number of jack of hearts, n(E)=1

Also, total number of cards, n(S)=52

∴  Probability of getting the jack of hearts =

n(E) / n(S)= 1 / 52

Hence, the required probability is  1 / 52

(iv) Probability of getting a red face card:

We know that, there are 26 red cards, 13 each of hearts and diamonds. Both hearts and diamonds have 3 face cards each.

∴  Number of red face cards, n(E)=6

Also, total number of cards, n(S)=52

∴  Probability of getting a red face card =

n(E) / n(S) = 6 / 52

⇒ 3 / 26

Hence, the required probability is  3 / 26

​(v) Probability of getting a spade:

We know that, there are 13 cards of spades.

∴  Number of spades, n(E)=13

Also, total number of cards, n(S)=52

∴  Probability of getting a spade =

n(E) / n(S) = 13 / 52

⇒ 1 / 4

Hence, the required probability is  1 / 4

(vi) Probability of getting the queen of diamonds:

We know that, there are 13 cards of diamonds. There is 1 queen of diamonds.

∴  Number of queens in diamonds, n(E)=1

Also, total number of cards, n(S)=52

∴  Probability of getting the queen of diamonds =

n(E) / n(S) = 1 / 52

​Hence, the required probability is  1/52

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