Question

Compute the probability of randomly drawing five cards with replacement from a standard deck and getting exactly two aces.

Answer 1

A standard deck of card box contain total 52 cards. And among them each suit has one ase so, total number of aces are 4.

A: event denoting that 5 cards are randomly selected from full pack of cards and among them exactly 2 are aces.

Now any random 5 cards from 52 cards can be selected 52C5 ways.

And 2 aces from 4 aces can be selected 4C2 ways.

And any random 3 cards from 48 cards can be selected 48C3 ways

So P(A) = (4C2 X 48C3)/52C5 = 103776/2598960 = 0.0399