you pick a card at random, put it back, and then pick another card at random. what is the probability of…

Explanation:

Step1: Calculate probability of picking 4

There are 3 cards, so the probability of picking a 4 on the first - draw is $\frac{1}{3}$.

Step2: Calculate probability of picking 3

Since the card is replaced, there are still 3 cards. The probability of picking a 3 on the second - draw is $\frac{1}{3}$.

Step3: Calculate joint probability

For independent events, the joint probability is the product of the individual probabilities. So the probability of picking a 4 and then a 3 is $\frac{1}{3}\times\frac{1}{3}$. $\frac{1}{3}\times\frac{1}{3}=\frac{1}{9}$

Answer:

$\frac{1}{9}$