Question

question 1 points 2
what is the probability of drawing a king and then a queen from a deck of cards with replacement?

○ \\(\frac{1}{169}\\)

○ \\(\frac{4}{663}\\)

○ \\(\frac{1}{221}\\)

○ \\(\frac{1}{4}\\)

Explanation:

Step1: Probability of drawing a King

A standard deck has 52 cards, and 4 Kings. So the probability of drawing a King is $\frac{4}{52}=\frac{1}{13}$.

Step2: Probability of drawing a Queen (with replacement)

After replacement, the deck is still 52 cards with 4 Queens. So the probability of drawing a Queen is also $\frac{4}{52}=\frac{1}{13}$.

Step3: Probability of both events (independent, so multiply)

The probability of drawing a King then a Queen with replacement is $\frac{1}{13} \times \frac{1}{13}=\frac{1}{169}$.

Answer:

A. $\frac{1}{169}$