Question

You draw two cards from a standard deck of 52 cards and do not replace the first one before drawing the second. Find the probability of drawing a 7 for the first card and a king for the second card. Round your answer to the nearest thousandth.

Answer 1

Answer: $\dfrac{4}{663}$

Step-by-step explanation:

Total number of cards in  a deck = 52

Number of cards having 7 on them = 4

Number of cards having king on them = 4

P(a 7 for first card)= $\dfrac{4}{52}=\dfrac{1}{13}$

Total cards left = 52-1=51

P( a 7 for first card | a king  for the second card) = $\dfrac{4}{51}$

Since , P(A and B) = P(B|A) X P(A)  [Conditional probability ]

Now , the probability of drawing a 7 for the first card and a king for the second card.  = P( a king for the second card | a 7 for first card )  x (P(a 7 for first card))

$=\dfrac{1}{13}\times\dfrac{4}{51}=\dfrac{4}{663}$

Hence, the required probability :  $\dfrac{4}{663}$