Question

You have a standard deck of 52 cards. You pick one card from the deck and then, without putting the first one back, pick a second card. What is the probability that both cards will be 9s?

Answer 1

Set up the two events
A = first card is a 9
B = second card is a 9

The probability for event A is
P(A) = 4/52
because there are four "9" cards out of 52 total

If event A happens first, and B follows, then the probability is
P(B|A) = 3/51
because there are 3 nines left over out of 52-1 = 51 total left over
No replacement has been made
The notation P(B|A) means "probability of event B given that event A has happened"

Multiply the probabilities
P(A and B) = P(A)*P(B|A)
P(A and B) = (4/52)*(3/51)
P(A and B) = (4*3)/(52*51)
P(A and B) = 12/2652
P(A and B) = 1/221
P(A and B) = 0.00452488687782

Rounded to 4 decimal places, the approximate answer is 0.0045
The exact answer as a fraction is 1/221