Question

From a well shuffled pack of 52 cards, one card is drawn at random. Find the

probability of getting (i) red card (ii) heart card (iii) red king (iv) face card

(v) number card​

Answer 1

Solution:

We know that one card is drawn at random from 52 shuffled cards. This implies that the total number of outcomes = 52:

⇒n(s) = 52

Now, let's see probability of getting each case:

(i) Red card:

Totally there are 26 red cards: 13 from red diamond and other 13 from red heart. This implies that the number of favourable outcomes = 26

⇒n(A) = 26

By using Probability formula, we have:

⇒ P(red card) = n(A)/n(S)

⇒ P(red card) = 26/52

⇒ P(red card) = 1/2

Therefore, Probability of getting red card = 1/2

(ii) Heart card:

There are totally 13 heart cards out of 52 cards. This implies that the number of favourable outcomes = 13.

⇒n(A) = 13

By using Probability formula, we have:

⇒ P(heart card) = n(A)/n(S)

⇒ P(heart card) = 13/52

⇒ P(heart card) = 1/4

Therefore, Probability of getting heart card = 1/4

(iii) Red king:

There are totally 2 red kings: one from red diamond, other from red heart. This implies that, number of favourable outcomes = 2

⇒n(A) = 2

By using Probability Formula, we have:

⇒ P(red king) = n(A)/n(S)

⇒ P(red king) = 2/52

⇒ P(red king) = 1/26

Therefore, Probability of getting red king = 1/26

(iv) Face card:

There are totally 12 face cards: King, Queen and Jack from all the four sets. This implies that, number of favourable outcomes = 12

By using probability formula, we have:

⇒ P(face card) = n(A)/n(S)

⇒ P(face card) = 12/52

⇒ P(face card) = 3/13

Therefore, Probability of getting a face card = 3/13

(v) Number card:

There are totally 36 number cards in the deck. Each set has number cards from 2 to 10 which is totally 9. So, totally in four sets, there are:

⇒ 9×4 = 36 cards.

⇒ Remember: Ace cards must be removed, since its not a number card.

This implies that number of favourable outcomes = 36

By using Probability Formula, we have:

⇒ P(number card) = n(A)/n(S)

⇒ P(number card) = 36/52

⇒ P(number card) = 9/13

Therefore, Probability of getting number card = 9/13

Hope it helps you!