Answer:
[tex]\frac{4}{221}\approx 0.0181[/tex].
Step-by-step explanation:
We have been given that you draw two cards from a standard deck of 52 cards. We are asked to find the probability of drawing a face card and then an ace consecutively from the deck without replacement.
We know that a standard deck contains 12 face cards.
So probability of drawing a face card would be number of face cards over total cards.
[tex]\text{P(Face card})=\frac{12}{52}[/tex]
[tex]\text{P(Face card})=\frac{3}{13}[/tex]
We know that there are 4 aces is a standard deck.
Since we are not not replacing cards, so total number of cards after 1st draw would be 51 cards.
[tex]\text{P(Ace})=\frac{4}{51}[/tex]
Probability of drawing a face card and then an ace consecutively from the deck without replacement would be product of both probabilities.
[tex]\text{P(Face card and Ace})=\frac{3}{13}\times \frac{4}{51}[/tex]
[tex]\text{P(Face card and Ace})=\frac{1}{13}\times \frac{4}{17}[/tex]
[tex]\text{P(Face card and Ace})=\frac{4}{221}[/tex]
Therefore, the probability of drawing a face card and then an ace consecutively from the deck without replacement is [tex]\frac{4}{221}\approx 0.0181[/tex].
