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

Explanation:

Step1: Calculate first - pick probability

There are 7 cards in total, and 3 of them are even numbers (4, 6, 8). The probability of picking an even - numbered card on the first pick is $P_1=\frac{3}{7}$.

Step2: Calculate second - pick probability

Since we do not put the first card back, there are now 6 cards left. If the first card was even, then there are 2 even - numbered cards left. The probability of picking an even - numbered card on the second pick given that the first card was even is $P_2=\frac{2}{6}=\frac{1}{3}$.

Step3: Calculate combined probability

For two dependent events, the probability of both events occurring is the product of their probabilities. So $P = P_1\times P_2=\frac{3}{7}\times\frac{1}{3}$. $P=\frac{3\times1}{7\times3}=\frac{1}{7}$.

Answer:

$\frac{1}{7}$