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

4/221

Explanation:

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Answer 2

`(4)/(221)\approx 0.0181`.

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})=(12)/(52)`

`\text{P(Face card})=(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})=(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})=(3)/(13)* (4)/(51)`

`\text{P(Face card and Ace})=(1)/(13)* (4)/(17)`

`\text{P(Face card and Ace})=(4)/(221)`

Therefore, the probability of drawing a face card and then an ace consecutively from the deck without replacement is
`(4)/(221)\approx 0.0181`.