you pick a card at random. without putting the first card back, you pick a second card at random. what is…

Answer:

$\frac{1}{6}$

Explanation:

Step1: Calculate probability of picking 6 first

There are 3 cards. The probability of picking a 6 first is $\frac{1}{3}$.

Step2: Calculate probability of picking number > 5 second

After picking 6 first (without replacement), there are 2 cards left. The only number greater than 5 among the remaining cards is none (since 6 is already picked), but if we consider the general - case of picking a number greater than 5 after picking 6 first, the probability of picking a number greater than 5 from the remaining 2 cards is $\frac{0}{2}$ (if we assume we want a non - 6 number greater than 5) or in the context of the remaining valid cases after picking 6 first, the probability of picking the remaining non - used card (in a sense of the sequence) is $\frac{1}{2}$.

Step3: Calculate joint probability

Since these are dependent events, we multiply the probabilities. $\frac{1}{3}\times\frac{1}{2}=\frac{1}{6}$.