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

Explanation:

Step1: Count prime - numbers

The prime numbers in the set {2, 3, 4, 5, 6, 7} are 2, 3, 5, 7. So there are 4 prime numbers out of 6 numbers.

Step2: Calculate first - pick probability

The probability of picking a prime number on the first pick is $\frac{4}{6}=\frac{2}{3}$.

Step3: Calculate second - pick probability

Since we do not replace the first card, there are 5 cards left. If the first card was prime, then there are 3 prime numbers left. So the probability of picking a prime number on the second pick given that the first pick was prime is $\frac{3}{5}$.

Step4: Calculate combined probability

By the multiplication rule for dependent events, the probability of picking a prime number and then another prime number is $\frac{2}{3}\times\frac{3}{5}=\frac{2\times3}{3\times5}=\frac{2}{5}$.

Answer:

$\frac{2}{5}$