Question

you pick a card at random. without putting the first card back, you pick a second card at random. what is the probability of picking an odd number and then picking an even number? simplify your answer and write it as a fraction or whole number.

Explanation:

Step1: Calculate probability of first - pick

There are 4 odd numbers (1, 3, 5, 7) out of 8 cards. So the probability of picking an odd - numbered card first, $P_1=\frac{4}{8}=\frac{1}{2}$.

Step2: Calculate probability of second - pick

After picking an odd - numbered card first (without replacement), there are 7 cards left and 4 even numbers (2, 4, 6, 8). So the probability of picking an even - numbered card second, $P_2 = \frac{4}{7}$.

Step3: Calculate combined probability

Since these are independent events in the sense of sequential non - replacement picking, the probability of both events occurring is the product of their individual probabilities. So $P = P_1\times P_2=\frac{1}{2}\times\frac{4}{7}=\frac{4}{14}=\frac{2}{7}$.

Answer:

$\frac{2}{7}$