What is the theoretical probability of picking a diamond from a standard deck of cards?
Answers
Probability of a diamond being drawn is as above, (1/13)(1/53). So total probability of either diamond or ace forming is
((1/53)(1/4))+((1/53)(1/13))
=1/53(1/4+1/13)
=1/53((17/52))
=17/(53*52)
=17/2500, approximately.
Answer:
Playing Cards Probability
Playing cards probability problems based on a well-shuffled deck of 52 cards.
Basic concept on drawing a card:
In a pack or deck of 52 playing cards, they are divided into 4 suits of 13 cards each i.e. spades ♠ hearts ♥, diamonds ♦, clubs ♣.
Cards of Spades and clubs are black cards.
Cards of hearts and diamonds are red cards.
The card in each suit, are ace, king, queen, jack or knaves, 10, 9, 8, 7, 6, 5, 4, 3 and 2.
King, Queen and Jack (or Knaves) are face cards. So, there are 12 face cards in the deck of 52 playing cards.
Worked-out problems on Playing cards probability:
1. A card is drawn from a well shuffled pack of 52 cards. Find the probability of:
(i) ‘2’ of spades
(ii) a jack
(iii) a king of red colour
(iv) a card of diamond
(v) a king or a queen
(vi) a non-face card
(vii) a black face card
(viii) a black card
(ix) a non-ace
(x) non-face card of black colour
(xi) neither a spade nor a jack
(xii) neither a heart nor a red king
Solution:
In a playing card there are 52 cards.
Therefore the total number of possible outcomes = 52
(i) ‘2’ of spades:
Number of favourable outcomes i.e. ‘2’ of spades is 1 out of 52 cards.
Therefore, probability of getting ‘2’ of spade
Number of favorable outcomes
P(A) = Total number of possible outcome
= 1/52
(ii) a jack
Number of favourable outcomes i.e. ‘a jack’ is 4 out of 52 cards.
Therefore, probability of getting ‘a jack’
Number of favorable outcomes
P(B) = Total number of possible outcome
= 4/52
= 1/13
(iii) a king of red colour
Number of favourable outcomes i.e. ‘a king of red colour’ is 2 out of 52 cards.
Therefore, probability of getting ‘a king of red colour’
Number of favorable outcomes
P(C) = Total number of possible outcome
= 2/52
= 1/26
(iv) a card of diamond
Number of favourable outcomes i.e. ‘a card of diamond’ is 13 out of 52 cards.
Therefore, probability of getting ‘a card of diamond’
Number of favorable outcomes
P(D) = Total number of possible outcome
= 13/52
= 1/4
(v) a king or a queen
Total number of king is 4 out of 52 cards.
Total number of queen is 4 out of 52 cards
Number of favourable outcomes i.e. ‘a king or a queen’ is 4 + 4 = 8 out of 52 cards.
Therefore, probability of getting ‘a king or a queen’
Number of favorable outcomes
P(E) = Total number of possible outcome
= 8/52
= 2/13