Question

Determine the probability of being dealt 4 Aces of cards, from a deck of 52 playing cards, with a replacement.

Answer 1

Before finding the probability of being dealt 4 Aces of cards, let's find the probability of being dealt an Ace card on each draw.

The probability of getting an specific card from a deck is given by the ratio between the amount of this specific card and the total amount of cards. We have 4 Aces in a deck, and 52 cards, therefore, the probability of getting an Ace is

`(4)/(52)=(1)/(13)`

Since the cards are replaced, it is the same probability of getting an Ace on each draw.

Each draw is an independent event, the probability of them happening simultaneously is given by their product. The probability of being dealt 4 Aces of cards with a replacement is

`(1)/(13)*(1)/(13)*(1)/(13)*(1)/(13)=(1)/(13^4)=(1)/(28561)=0.00003501277\ldots`