4/221
The probability of drawing aces on the first three draws is approx 0.0001810
The probability of drawing three black cards from a standard pack depends on:whether the cards are drawn at random,whether or not the drawn cards are replaced before the next card is drawn,whether the probability that is required is that three black cards are drawn after however many draws, or that three black cards are drawn in a sequence at some stage - but not necessarily the first three, or that the first three cards cards that are drawn are black.There is no information on any of these and so it is not possible to be certain about the answer.The probability of drawing three black cards, in three random draws - without replacement - from a standard deck, is 0.1176 approx.
If only two cards are drawn from a standard deck of cards, with the first card replaced before drawing the second, the answer is 0.005917 (approx). If the first card is not replaced, the probability increases to 0.006033.
1-221
The probability of drawing the two of hearts is 1/52. The probability of drawing two cards that are hearts depends on whether or not the first card is replaced. If it is replaced, then the probability is (1/4)*(1/4) = 1/16 = 0.0625 while if it is not, the probability is (1/4)*(12/51) = 3/51 = 0.0588 (approx).
The probability of drawing aces on the first three draws is approx 0.0001810
The probability of drawing three black cards from a standard pack depends on:whether the cards are drawn at random,whether or not the drawn cards are replaced before the next card is drawn,whether the probability that is required is that three black cards are drawn after however many draws, or that three black cards are drawn in a sequence at some stage - but not necessarily the first three, or that the first three cards cards that are drawn are black.There is no information on any of these and so it is not possible to be certain about the answer.The probability of drawing three black cards, in three random draws - without replacement - from a standard deck, is 0.1176 approx.
The probability of drawing the first face card is 12 in 52. The probability of drawing the second is 11 in 51. The probability of drawing the third is 10 in 50. Thus, the probability of drawing three face cards is (12 in 52) times (11 in 51) times (10 in 50) or (1320 in 132600) or about 0.009955.
1/48 if there aren't jokers
The probability of drawing 2 cards that are two's from a standard deck of 52 playing cards is 1 in 221. The probability of drawing the first two is 4 in 52 or 1 in 13. The probability of drawing the second two is 3 in 51. Multiply those two probabilities together and you get 3 in 663, or 1 in 221.
Let's call the chance of drawing a 9 on the first draw P(A). Since there are four 9s, P(A) is 4/52. Probability of not drawing a 9 is 1-(4/52). Each draw is independent so we multiply the probabilities. The probability of EXACTLY one 9 in two draws if P(A)P(1-A)=12/169 which is a about .071
If only two cards are drawn from a standard deck of cards, with the first card replaced before drawing the second, the answer is 0.005917 (approx). If the first card is not replaced, the probability increases to 0.006033.
There are 26 red cards and 13 spades in a standard deck of 52 cards. The probability of drawing a red card or a spade in one draw is, therefore, 39 in 52. If you draw twocards, and the first is not red or spade, then the probability on the second draw is 39 in 51, otherwise it is 38 in 51.Combining these two probabilities is easy. Just turn the problem around, and ask what is the probability of drawing two clubs? The answer is (13 in 52) times (12 in 51), which is 156 in 2652, or 1 in 17. Flip that answer over by subtracting it from 1, and you get a probability of drawing a red card or a spade in two draws of 16 in 17, or about 0.9412.
1-221
The probability of drawing the two of hearts is 1/52. The probability of drawing two cards that are hearts depends on whether or not the first card is replaced. If it is replaced, then the probability is (1/4)*(1/4) = 1/16 = 0.0625 while if it is not, the probability is (1/4)*(12/51) = 3/51 = 0.0588 (approx).
In order to determine the probability of drawing 2 hearts and then a spade, in that order, from a deck of 52 cards, start by considering the first card. The probability of drawing a heart is 1 in 4. Since you have now reduced the number of hearts and the number of cards in the deck by one, the probability of drawing another heart is 4 in 17. Since you have further reduced the number of cards by one, the probability of drawing a spade is 13 in 50. Multiply these probabilities together, (1/4) (4/17) (13/50), and you get about 0.0153, or about 153 in 10000.
The probability of doing so, if the first card is not replaced, is 0.0385, approx.