Calculating Probability of Drawing Cards from a Deck

In summary, the conversation discusses drawing cards from a 52 card deck and calculating the probability of certain outcomes. The first question asks for the probability of drawing one black card and one red card, while the second question asks for the probability of both cards being the same color. Lastly, the conversation touches on the importance of understanding combinatorics in solving these types of probability problems.
  • #1
mayra1223
1
0
Drawing cards:
Two cards are drawn from a 52 card deck. What is the probability that
A. 1 card is black and 1 card is red
B. Both cards are the same color
C. Both cards are red?

Please I need help
Thank youu
 
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  • #2
Let's start easy: Suppose I draw just one, what is the chance that it is black?
Now, I have a deck with 51 cards, of which 26 are red and 25 black. I draw one, what is the chance that it is red? Now what is the chance that both happen in sequence?
Now do the same for the case where the red one is drawn first, and add the probabilities.
 
  • #4
mayra1223 said:
Drawing cards:
Two cards are drawn from a 52 card deck. What is the probability that
A. 1 card is black and 1 card is red
B. Both cards are the same color
C. Both cards are red?

Please I need help
Thank youu
I have never understood much about probability; could you please offer me some clues, for example by posting what you have done so far?

You shouldn't expect people to manage this without your cooperative help! :smile:
 
  • #5
CompuChip said:
Let's start easy: Suppose I draw just one, what is the chance that it is black?
Now, I have a deck with 51 cards, of which 26 are red and 25 black. I draw one, what is the chance that it is red? Now what is the chance that both happen in sequence?
Now do the same for the case where the red one is drawn first, and add the probabilities.

As CompuChip suggested, try the above method and post what you get. You might also want to familiarize and brush up on combinatorics. If you know how to calculate permutation and combination, it should be good, at least for now. This makes your job "slightly" easier in the above problem, and very easy in problems like, choosing four cards from 52 each of different suite. In that case, it can take a while to calculate the various ways of suite selection (i.e. first hearts, then spades etc. and also other combinations).

But if your combinatorics is good, then you can directly use those concepts in calculating Probability, that makes your life easier.

Regards,
Sleek.
 

1. What is the definition of probability when drawing cards?

Probability in this context refers to the likelihood of drawing a certain card or set of cards from a deck. It is calculated by dividing the number of desired outcomes by the total number of possible outcomes.

2. How do you calculate the probability of drawing a specific card?

To calculate the probability of drawing a specific card, divide the number of that card in the deck by the total number of cards in the deck. For example, if you have a standard deck of 52 cards and want to know the probability of drawing a King, you would divide 4 (the number of Kings in a deck) by 52, which equals 0.077 or 7.7%.

3. What is the formula for calculating the probability of drawing multiple cards in a row?

The formula for calculating the probability of drawing multiple cards in a row is to multiply the probabilities of each individual draw. For example, if you want to know the probability of drawing a King and then a Queen from a standard deck of 52 cards, you would multiply 4/52 (probability of drawing a King) by 4/51 (probability of drawing a Queen from the remaining 51 cards), which equals 0.006 or 0.6%.

4. How does the probability of drawing cards change as cards are drawn?

The probability of drawing cards changes as cards are drawn because the total number of cards in the deck decreases with each draw. This means that the number of desired outcomes also decreases, resulting in a lower probability of drawing a specific card. For example, in a standard deck of 52 cards, the probability of drawing an Ace on the first draw is 4/52 (7.7%), but on the second draw, it becomes 4/51 (7.8%) because there is now one less Ace in the deck.

5. Can probability be used to predict the exact order in which cards will be drawn?

No, probability cannot be used to predict the exact order in which cards will be drawn. While it can tell you the likelihood of drawing a certain card, it cannot determine the exact order in which the cards will appear. This is because each draw is independent and previous draws do not affect future ones.

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