Probability of deck of cards question

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The discussion centers on calculating the probability of drawing two red cards and two picture cards from a standard deck of cards. The initial calculations provided include the probabilities for drawing the first and second red cards, as well as the first and second picture cards. Participants question how to combine these probabilities, with some confusion around joint probability and whether to replace cards after drawing. Clarifications are provided regarding the composition of the deck, specifically the number of picture cards and red cards. The conversation highlights a need for understanding basic probability concepts in the context of card games.
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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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I don't know joint probability. But you can get the answer by multiplying the numbers together.
 
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)
 
Do you replace the first card once picked out of the deck?
 
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.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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