SOLUTION: What is the probability of drawing three queens from a standard deck of cards, given that the first card drawn was a queen? Assume that the cards are not replaced.

Question 1137617: What is the probability of drawing three queens from a standard deck of cards, given that the first card drawn was a queen? Assume that the cards are not replaced.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

The first card drawn was a queen
So we have 52-1 = 51 cards left, 4-1 = 3 of which are queens.

The probability of a queen on the second draw is 3/51 since there are 3 cards we want out of 51 total.

Then the probability of another queen after that is 2/50 since there are 2 queens left and 50 cards total (3-1 = 2; 51-1 = 50)

Multiplying those fractions out gives us
(3/51)*(2/50) = (3*2)/(51*50) = 6/2550 = 1/425

The answer as a fraction is 1/425
The answer in decimal form is roughly 0.00235
This converts to 0.235%

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