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

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 even number and then picking an odd number? write your answer as a fraction or whole number.

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 even number and then picking an odd number? write your answer as a fraction or whole number.

Answer

Explanation:

Step1: Calculate first - pick probability

There are 4 even numbers (2, 4, 6, 8) out of 8 cards. So the probability of picking an even number first is $\frac{4}{8}=\frac{1}{2}$.

Step2: Calculate second - pick probability

After picking an even - numbered card first without replacement, there are 7 cards left, and 4 odd numbers (3, 5, 7, 9). So the probability of picking an odd number second is $\frac{4}{7}$.

Step3: Calculate combined probability

Since these are dependent events, we multiply the probabilities of each event. The probability of picking an even number first and then an odd number is $\frac{1}{2}\times\frac{4}{7}=\frac{4}{14}=\frac{2}{7}$.

Answer:

$\frac{2}{7}$