Question

You draw two cards from a standard deck of 52 cards. What is the probability of drawing a face card and then an ace consecutively from the deck without replacement?

Answer 1

Answer:

$\frac{4}{221}\approx 0.0181$.

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.

$\text{P(Face card})=\frac{12}{52}$

$\text{P(Face card})=\frac{3}{13}$

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.

$\text{P(Ace})=\frac{4}{51}$

Probability of drawing a face card and then an ace consecutively from the deck without replacement would be product of both probabilities.

$\text{P(Face card and Ace})=\frac{3}{13}\times \frac{4}{51}$

$\text{P(Face card and Ace})=\frac{1}{13}\times \frac{4}{17}$

$\text{P(Face card and Ace})=\frac{4}{221}$

Therefore, the probability of drawing a face card and then an ace consecutively from the deck without replacement is $\frac{4}{221}\approx 0.0181$.

Answer 2

Answer:

4/221

Step-by-step explanation:

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