Three cards are drawn without replacement from an ordinary deck of 52 playing cards. What is the probability that the second and third cards are kings if the first card was not a king?
After the first card is drawn, there are 4 kings in a 51 card deck. There is therefore a 4/51 probability that the next card is a king. When that happends, there is a 3/50 probability that the third card is a ling.
So, multiply 4/51 by 3/50 for your answer. The fraction that you should be reduced to lowest terms.
http://www.webmath.com/redfract.html
To find the probability that the second and third cards are kings given that the first card was not a king, we need to consider the total number of possible outcomes and the number of favorable outcomes.
First, let's calculate the total number of possible outcomes. We have already drawn the first card, so there are 51 cards remaining to be drawn for the second card, and 50 cards remaining for the third card. Thus, the total number of possible outcomes is (51 * 50) = 2550.
Now, let's calculate the number of favorable outcomes. Since the first card was not a king, there are 48 non-king cards remaining in the deck. Out of these 48 cards, 4 are kings. So, for the second card, we have 4 favorable kings out of 48 non-king cards (48 * 4). For the third card, we have 3 favorable kings out of 47 remaining cards (47 * 3). Therefore, the number of favorable outcomes is (48 * 4 * 47 * 3) = 27,216.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes
Probability = 27,216 / 2550
Probability = 0.1067 (approximately, rounded to four decimal places)
So, the probability that the second and third cards are kings given that the first card was not a king is approximately 0.1067, or 10.67%.