1. A standard card deck has 52 cards, 13 cards in each of four \"suits\" (Spades
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Question
1. A standard card deck has 52 cards, 13 cards in each of four "suits" (Spades, Hearts, Clubs 2 and Diamonds). Each "suit" of 13 cards is sequentially "numbered" Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King. The order of the cards in the deck is randomized by thorough "shuffling" and the cards are placed face down on a table. Without looking at any of the cards in one standard card deck: a What is the probability that the deck's top card is the King of Hearts (King in the "suit of Hearts)? b) What is the probability that the deck's bottom card is the King of Hearts? c) What is the probability there is a King of Hearts in the deck? d) What is the probability there is no "King of Hearts" in the deck? If the top card is revealed by turning it over, face up: e What is the probability that deck's bottom card is the Queen of Hearts if the top card is the King of Hearts? that the deck's top card will be the Ace of Clubs again? has been randomized, what is the probability that the top card on both decks is the f) If the top card is the Ace of Clubs, and the deck is shuffled again, what are the odds g) If there are two identical sets (decks) of cards and the order of the cards in each declk Two of Diamonds?Explanation / Answer
a)
There are total 52 cards in the deck. Out of 52 cards, one is king of heart. That is out of 52 possibilites of top cards, one is king of heart so the required probability is
P(top is king of heart) = 1/52
b)
There are total 52 cards in the deck. Out of 52 cards, one is king of heart. That is out of 52 possibilites of bottom card, one is king of heart so the required probability is
P(bottom is king of heart) = 1/52
c)
There is definetly a card numbered as king of heart so it is certain event. Therefore the required probability is
P(king of heart in deck) = 1
d)
By the complement rule,
P(no king of heart in deck) =1- P(king of heart in deck) = 0
e)
Since it is given that top card is King of hearts so for bottom card 51 possibilites are remaining out of which one is Queen of hearts so
P(Bottom Queen of heart | top is King of heart) = 1/51
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