Question

you randomly shuffle a standard deck of cards with no jokers. this deck has 4 suits (diamonds, spades, hearts, clubs), with 13 cards per suit (numbers 2 through 10, jack, queen, king, ace), which add up to 52 cards in total. after shuffling, you deal two cards from the top. what is the probability that you deal a king followed by a jack? submit your answer as a simplified fraction or a decimal rounded to 4 decimal places.

Explanation:

Step1: Calculate probability of first - card being a King

There are 4 Kings in a 52 - card deck. The probability of drawing a King first is $\frac{4}{52}=\frac{1}{13}$.

Step2: Calculate probability of second - card being a Jack given first was a King

After drawing a King first, there are 51 cards left in the deck. There are 4 Jacks. So the probability of drawing a Jack second, given that the first card was a King, is $\frac{4}{51}$.

Step3: Calculate the joint probability

By the multiplication rule for dependent events, the probability of drawing a King followed by a Jack is the product of the probabilities of each event. So $P=\frac{1}{13}\times\frac{4}{51}=\frac{4}{663}\approx0.0060$

Answer:

$\frac{4}{663}\approx0.0060$