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You are dealt two cards successfuly without replacement from a shuffled deck of 52 playing card. Find the probability that first card is a king and the second card is a queen. Express your answer as a simplified fraction

Answer :

The simplified expression is [tex](\frac{4}{663})[/tex]

Step-by-step explanation:

Here, the total number of cards in a given deck = 52

let E : Event of drawing a first card which is King

Total number of kings in the given deck = 4

So, [tex]P(E) = \frac{\textrm{The total number of king}}{\textrm{The total number of cards}}[/tex] = [tex]\frac{4}{52} = (\frac{1}{13} )[/tex]

Now, as the picked card is NOT REPLACED,

So, now the total number of cards = 52 - 1 = 51

Total number of queen in the deck is same as before = 13

let K : Event of drawing a second card which is queen

So, [tex]P(K) = \frac{\textrm{The total number of queen}}{\textrm{The total number of cards}}[/tex] = [tex](\frac{4}{51} )[/tex]

Now, the combined probability of picking first card as king and second as queen  = P(E) x P(K)  = [tex](\frac{1}{13}) \times(\frac{4}{51}) = (\frac{4}{663} )[/tex]

Hence, the simplified expression is [tex](\frac{4}{663})[/tex]

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