Question

Three cards are drawn from an ordinary deck without replacement. Whats the probability of getting all queens?

Answer 1

At any point the probability of drawing a queen is: (number of queens in the deck)/(the total number of cards in the deck)<br> At the beginning there are a total of 52 cards and 4 queens. So the probability of drawing a queen on the first draw is: 4/52 = 1/13<br> Since there is no replacement, the deck now has 51 cards and, if we drew a queen, there are only 3 queens remaining. So the probability of drawing a queen on the second draw is: 3/51 = 1/17<br> Since there is no replacement, the deck now has 50 cards and, if we have drawn 2 queens so far, there are only 2 queens remaining. So the probability of drawing a queen on the third draw is: 2/50 = 1/25<br> The probability of all three events (queen on the first draw, queen on the second draw and queen on the third draw) is the product of their probabilities: (1/13)*(1/17)*(1/25) = 1/5525