using a deck of cards,what is the probability that you would pull a red kind and a black queen in two pulls without replacing the first card back into the deck?
I believe you mean read KING, not red KIND. There are two red kings and two black queens. The probability of drawing either one, in a single draw, is 2/52 = 1/26.
There are two ways you could end up with one black queen and one red king: You could get the king first or the queen first. The total probability is
2*(1/26)^2 = 1/338
Since you are not replacing the card, the prob of the second draw is different from the first draw.
could be RK,BQ or BW,RK
prob of that is (2/52)(2/51) + (2/52)(2/51)
= 2(2/52)(2/51) = 2/663
or
choose a red king -->C(4,2) = 2
choose a black queen --> C(4,2) = 2
choose any two cards --> C(52,2) = 1326
prob = 2*2/1326 = 2/663
Reiny is correct; I missed the word "without" (replacing).
To determine the probability of pulling a red king and a black queen in two pulls without replacement from a standard deck of cards, we need to calculate the probability of each individual event and then multiply those probabilities.
First, let's figure out the probability of pulling a red king on the first draw. In a standard deck, there are 2 red kings (hearts and diamonds) out of a total of 52 cards. So the probability of drawing a red king on the first draw is 2/52, which simplifies to 1/26.
Next, let's determine the probability of pulling a black queen on the second draw. After removing the first card, there are now 51 cards left in the deck, with 2 black queens (spades and clubs). So the probability of drawing a black queen on the second draw is 2/51.
To find the probability of both events occurring, we need to multiply the probabilities together. Therefore, the probability of pulling a red king and a black queen in two draws without replacement is (1/26) * (2/51).
To simplify this probability, we can multiply both numerators and both denominators together: 2/1326.
Therefore, the probability of pulling a red king and a black queen in two draws without replacement from a deck of cards is 2/1326, which can also be simplified as 1/663.