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

Explanation:

Step1: Calculate first - pick probability

There are 7 cards in total, and 3 even - numbered cards (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 the first card is not replaced, there are 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 joint probability

The probability of both events happening is the product of the probabilities of each event. Using the multiplication rule for dependent events $P = P_1\times P_2$. Substitute $P_1=\frac{3}{7}$ and $P_2=\frac{1}{3}$ into the formula: $P=\frac{3}{7}\times\frac{1}{3}=\frac{3\times1}{7\times3}=\frac{1}{7}$.

Answer:

$\frac{1}{7}$