Question

three cards are drawn all at once from a standard deck of 52 playing cars. What is the probability of selecting exactly two aces?

Answer 1

16/2704 = 1/169 = .59%

Answer 2

Just over half a percent chance. Seems about right.

Answer 3

where did you get the 15/2704?

Answer 4

(4/52)^2

Answer 5

yet when I check my answer to this i see that the answer you give is different than the given answer

Answer 6

or you can do (1/13)^2 = (1/169)

Answer 7

What answer did you get?

Answer 8

the answer given in the book is 0.013

Answer 9

Let A=ace and B=any card, you're looking for the outcomes:
AAB,ABA,BAA in a draw, the order in which the cards are drawn being trivial.

Let's take one for example, AAB.
You draw one of four aces from a deck of 52, then one of three aces from a deck of 51 (you already removed one card) then one of the other 48 cards from a deck of 50.
So, \[P(AAB)=\frac{4}{52} \times \frac{3}{51} \times \frac{48}{50}=\frac{4*3*48}{52*51 *50}\]
One sees afterwards that the result is the same for P(ABA) and P(BAA).

So you have
\[P(two\ aces\ and\ one\ card)=3 \times \frac{4 \times 3 \times 48}{52 \times 51 \times 50}\]
Evaluate and you get 0,013 (approx)