Question

find the indicated probability. you are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. find the probability that the first card is a king and the second card is a jack. express your answer as a simplified fraction. $\frac{2}{13}$ $\frac{103}{663}$ $\frac{1}{2}$ $\frac{4}{663}$

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 $P(\text{King})=\frac{4}{52}=\frac{1}{13}$.

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

Since the first card is not replaced, there are now 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 $P(\text{Jack}|\text{King})=\frac{4}{51}$.

Step3: Use the multiplication rule for dependent events

The probability of both events occurring is $P(\text{King and Jack}) = P(\text{King})\times P(\text{Jack}|\text{King})=\frac{1}{13}\times\frac{4}{51}=\frac{4}{663}$.

Answer:

$\frac{4}{663}$