A card is drawn from a deck of 52 cards . Find the probability of getting a two digit number card
Answers
Answer:
Given that, one card is drawn from a well shuffled deck of 52 cards.
To find out: The probability of getting:
(i) A king of red colour,
(ii) A face card,
(iii) The jack of hearts,
(iv) A red face card,
(v) A spade,
(vi) The queen of diamonds.
We know that,
The probability of an event E,P(E)=
Total number of outcomes
Number of favourable outcomes
=
n(S)
n(E)
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(S)
n(E)
=
52
2
⇒
26
1
Hence, the required probability is
26
1
.
(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(S)
n(E)
=
52
12
⇒
13
3
Hence, the required probability is
13
3
.
(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(S)
n(E)
=
52
1
Hence, the required probability is
52
1
.
(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(S)
n(E)
=
52
6
⇒
26
3
Hence, the required probability is
26
3
.
(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(S)
n(E)
=
52
13
⇒
4
1
Hence, the required probability is
4
1
.
(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(S)
n(E)
=
52
1
Hence, the required probability is
52
1
.
Answer:
26% is can be the probability of52