Question

Three cards are dealt from a shuffled standard deck of playing cards. What is the probability that the three cards dealt are in order, an ace, a face card, and a 2 card? (Face card being Jack queen and king)

Answer 1

To do this exercise we have to calculate each event's probability.

So:

1. Probability it is an ace: 1/13

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

2. Probability of a face-card

In this case the:e are 51 cards remaining

`(12facecards)/(51playingcards)=\text{ }(12)/(51)`

3. Probability of a two-card:

In this case, there are 50 cards remaining

`(4`

So, the probability of them happening in order is the product of the three. So:

`(1)/(13)((12)/(51))((2)/(25))=(24)/(16575)=(8)/(5525)\text{ We simplify by 3}`

The probability is 8/5525 or 0.00145 or 0.0145%