giulia is playing a game with 6 cards: 4 kings, 1 queen, and 1 jack. she draws 1 card out of the stack of…

giulia is playing a game with 6 cards: 4 kings, 1 queen, and 1 jack. she draws 1 card out of the stack of cards, replaces it, and then draws another card. what is the probability that she will draw a king and then a jack, p(king, then jack)?\n\\(\\frac{1}{36}\\)\n\\(\\frac{1}{24}\\)\n\\(\\frac{1}{9}\\)\n\\(\\frac{1}{6}\\)

giulia is playing a game with 6 cards: 4 kings, 1 queen, and 1 jack. she draws 1 card out of the stack of cards, replaces it, and then draws another card. what is the probability that she will draw a king and then a jack, p(king, then jack)?\n\\(\\frac{1}{36}\\)\n\\(\\frac{1}{24}\\)\n\\(\\frac{1}{9}\\)\n\\(\\frac{1}{6}\\)

Answer

Explanation:

Step1: Calculate probability of drawing a king

There are 4 kings out of 6 cards. So the probability of drawing a king, $P(\text{king})=\frac{4}{6}=\frac{2}{3}$.

Step2: Calculate probability of drawing a jack

There is 1 jack out of 6 cards. So the probability of drawing a jack, $P(\text{jack})=\frac{1}{6}$.

Step3: Calculate combined probability

Since the draws are independent (because the card is replaced), we multiply the probabilities. $P(\text{king, then jack}) = P(\text{king})\times P(\text{jack})=\frac{2}{3}\times\frac{1}{6}=\frac{2}{18}=\frac{1}{9}$.

Answer:

$\frac{1}{9}$