Question

1. what is the probability of drawing two cards of the same rank in a row with replacement?

Explanation:

Step1: Understand the deck

A standard deck has 52 cards, 13 ranks (2 - Ace), 4 suits per rank.

Step2: Probability of first card

Probability of drawing any card: $P_1=\frac{52}{52} = 1$ (since we can draw any card first).

Step3: Probability of second card (with replacement)

After replacing the first card, the deck is back to 52. To match the rank of the first card, there are 4 cards of that rank. So $P_2=\frac{4}{52}=\frac{1}{13}$.

Step4: Multiply probabilities (independent events)

Since the draws are with replacement, the events are independent. So total probability $P = P_1\times P_2=1\times\frac{1}{13}=\frac{1}{13}$.

Answer:

$\frac{1}{13}$