you pick a card (4, 5, 6) at random. without putting the first card back, you pick a second card at random…

Explanation:

Step1: Calculate probability of picking 5 first

There are 3 cards (4, 5, 6). The probability of picking a 5 on the first - draw is $\frac{1}{3}$.

Step2: Calculate probability of picking 6 second

After picking a 5 on the first draw (without replacement), there are 2 cards left. The probability of picking a 6 on the second draw is $\frac{1}{2}$.

Step3: Calculate joint - probability

Since these are dependent events, the probability of both events occurring is the product of their individual probabilities. So $P = \frac{1}{3}\times\frac{1}{2}=\frac{1}{6}$.

Answer:

$\frac{1}{6}$