Question

25. Compute the probability that a five-card poker hand is dealt to you that contains 4 Aces.

Answer 1

The calculated probability of 4 Aces is 0.00000369378

Computing the probability of 4 Aces.

From the question, we have the following parameters that can be used in our computation:

Cards = 52

Aces = 4

Using the above as a guide, we have the following:

P(4 Aces) = 4/52 * 3/51 * 2/50 * 1/49

Evaluate the products

P(4 Aces) = 0.00000369378

Hence, the probability of 4 Aces is 0.00000369378

Answer 2

The standard deck of cards has 52 different cards.

4 of these cards are aces.

For the first card, the probability of having an ace is 4/52, since there are 4 aces still available.

Then, for the second card, the probability will be 3/52, because one of the aces is already picked.

Similarly, the third ace has a probability of 2/52 and the last ace has a probability of 1/52.

The final probability will be:

`P=(4\cdot3\cdot2\cdot1)/(52\cdot52\cdot52\cdot52)=(3)/(52\cdot52\cdot26\cdot13)=(3)/(913952)`