Four cards are dealt from a standard fifty-two-card poker deck. what is the probability that all four are aces given that at least three are aces? (note: there are 270,725 different sets of four cards that can be dealt. assume that the probability associated with each of those hands is 1/270,725.) larsen, richard j.. an introduction to mathematical statistics and its applications (p. 38). pearson education. kindle edition.

The probability is 0.0052

Step-by-step explanation:

Let's call A the event that the four cards are aces, B the event that at least three are aces. So, the probability P(A/B) that all four are aces given that at least three are aces is calculated as:

P(A/B) =  P(A∩B)/P(B)

The probability P(B) that at least three are aces is the sum of the following probabilities:

So, the number of ways to select exactly 3 aces is:

Because we are going to select 3 aces from the 4 in the poker deck and we are going to select 1 card from the 48 that aren't aces. So the probability in this case is 192/270,725

Then, the probability P(B) that at least three are aces is:

On the other hand the probability P(A∩B) that the four cards are aces and at least three are aces is equal to the probability that the four card are aces, so:

P(A∩B) = 1/270,725

Finally, the probability P(A/B) that all four are aces given that at least three are aces is:

the 4th choice is the correct one

step-by-step explanation:

idk

step-by-step explanation:

i don't know