Probability of deck of cards question

In summary, the probability of obtaining two red cards (A-10 hearts or diamonds) and two picture cards (any suit) in any order from a deck of cards is calculated by multiplying the probabilities of drawing a red card and a picture card for each draw. The probability of drawing a red card on the first draw is 20/52, and then 19/51 for the second draw. The probability of drawing a picture card on the first draw is 12/52, and then 11/51 for the second draw. This can be simplified to (20/52)*(19/51)*(12/52)*(11/51) = 0.1109, or approximately 11.1%. There are four
  • #1
nikk834
27
0

Homework Statement



Use probability trees to determine the probability of obtaining,in a deck of cards:

two red cards (A-10 hearts or diamonds) and two picture cards (any suit) in any order?

Homework Equations





The Attempt at a Solution


P(1st red card)= 20/52 P (2nd red card)=19/51
P(1st picture card) = 12/52 P(2nd picture card)=11/51
How would you combine these together to get the solution? Do you use joint probability?
 
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  • #2
I don't know joint probability. But you can get the answer by multiplying the numbers together.
 
  • #3
I don't know much about cards (can you tell me how many picture cards and how many color cards are there in a deck)
 
  • #4
Do you replace the first card once picked out of the deck?
 
  • #5
snshusat161 said:
I don't know much about cards (can you tell me how many picture cards and how many color cards are there in a deck)

Are you serious you don't know? There are Jacks, Queens and Kings (picture), Ace's, 2-10's. Four of each.
 

1. What is the probability of drawing a specific card from a deck?

The probability of drawing a specific card from a deck depends on the total number of cards in the deck and the number of cards that match the specific card. For example, if there are 52 cards in the deck and 4 cards of the same rank, the probability would be 4/52 or approximately 7.7%.

2. What is the probability of drawing a certain hand from a deck?

The probability of drawing a certain hand from a deck depends on the specific hand and the total number of possible hands in a deck. For example, the probability of drawing a three of a kind hand from a deck of 52 cards would be 2.1%.

3. How is the probability of drawing a card affected by previous draws?

The probability of drawing a card is not affected by previous draws, as the deck is randomly shuffled before each draw. Each card has an equal chance of being drawn regardless of previous draws.

4. What is the probability of drawing a card of a specific suit from a deck?

The probability of drawing a card of a specific suit from a deck depends on the total number of cards in the deck and the number of cards that belong to the specific suit. For example, if there are 52 cards in the deck and 13 cards of the same suit, the probability would be 13/52 or approximately 25%.

5. How does the number of decks in play affect the probability of drawing a specific card?

The number of decks in play does not affect the probability of drawing a specific card, as long as the decks are shuffled and combined before drawing. Each card still has an equal chance of being drawn regardless of the number of decks in play.

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