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

Answer

Explanation:

Step1: Calculate probability of first - pick

There are 2 odd numbers (5, 7) out of 4 cards. So the probability of picking an odd number first is $\frac{2}{4}=\frac{1}{2}$.

Step2: Calculate probability of second - pick

After picking an odd number first (without replacement), there are 3 cards left. There are 2 even numbers (6, 8) out of the remaining 3 cards. So the probability of picking an even number second is $\frac{2}{3}$.

Step3: Calculate joint probability

Since these are independent - like events (in the sense of sequential non - replacement picking), we multiply the probabilities of each event. So the probability of picking an odd number and then an even number is $\frac{1}{2}\times\frac{2}{3}=\frac{1\times2}{2\times3}=\frac{1}{3}$.

Answer:

$\frac{1}{3}$