Probability of card shuffling homework

In summary, the probability of obtaining four red cards (not including JQK hearts or JQK diamonds) from a deck of cards that is shuffled and dealt four times can be calculated using a probability tree. The exact calculation will depend on whether or not the JQK hearts and diamonds are included in the deck or not.
  • #1
nikk834
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Homework Statement


A deck of cards is shuffled and a card is dealt. The remaining cards are shuffled and another card is dealt. The process is repeated until you have four cards dealt from the main pack. Use probability trees to determine the probability of obtaining:

four red cards (not including JQK hearts or JQK diamonds)?

Homework Equations





The Attempt at a Solution



For this would you put 20/46, 19/45, 18/44 and 17/43 or would you put the 20/52, 19/51, 18/50,17/49?
 
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  • #2


Well, it depends on the question. By "(not including JQK hearts or JQK diamonds)", does it mean not to use them at all in the deck or they are used but just don't count as red cards.
 

FAQ: Probability of card shuffling homework

What is the probability of getting a specific card after shuffling a deck?

The probability of getting a specific card after shuffling a deck is 1/52 or approximately 0.0192. This assumes that the deck is being shuffled randomly and effectively.

How many shuffles are needed for a deck of cards to be considered truly random?

The number of shuffles needed for a deck of cards to be considered truly random is debated among mathematicians. Some believe that seven shuffles are enough, while others argue that up to 12 shuffles may be needed.

What is the difference between a perfect shuffle and a riffle shuffle?

A perfect shuffle involves dividing the deck exactly in half and interleaving the cards from each half. This results in the top and bottom cards remaining in their original positions. A riffle shuffle involves dividing the deck into two unequal stacks and then merging them together by interleaving the cards. This results in the top and bottom cards being mixed up.

Does the order of the cards matter when calculating the probability of a specific card?

Yes, the order of the cards does matter when calculating the probability of a specific card. For example, if a card is placed at the bottom of the deck after shuffling, the probability of drawing that card will be lower compared to if it was near the top of the deck.

How does the number of cards in a deck affect the probability of drawing a specific card?

The number of cards in a deck does not affect the probability of drawing a specific card. As long as the deck is shuffled effectively, each card will have an equal chance of being drawn regardless of the number of cards in the deck.

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