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

The odd numbers are 5 and 7. There are 2 odd numbers out of 4 cards. So the probability of picking an odd number first, $P_1=\frac{2}{4}=\frac{1}{2}$.

Step2: Calculate second - pick probability

After picking an odd number first (without replacement), there are 3 cards left. The even numbers are 4 and 6. So there are 2 even numbers out of 3 remaining cards. The probability of picking an even number second given that an odd number was picked first, $P_2 = \frac{2}{3}$.

Step3: Calculate joint probability

Since these are dependent events, the probability of both events occurring is the product of their probabilities. $P = P_1\times P_2=\frac{1}{2}\times\frac{2}{3}=\frac{1\times2}{2\times3}=\frac{1}{3}$.

Answer:

$\frac{1}{3}$