you pick a card (1, 2, 3, 4, 5, 6) at random. without putting the first card back, you pick a second card at…

Explanation:

Step1: Calculate first - pick probability

The odd numbers in the set {1, 2, 3, 4, 5, 6} are 1, 3, 5. So there are 3 odd numbers out of 6. The probability of picking an odd number on the first pick, $P_1=\frac{3}{6}=\frac{1}{2}$.

Step2: Calculate second - pick probability

Since we do not put the first card back, there are now 5 cards left. If the first - picked card was odd, then there are 2 odd numbers left. So the probability of picking an odd number on the second pick given that the first pick was odd, $P_2=\frac{2}{5}$.

Step3: Calculate combined probability

For two dependent events, the probability of both events occurring is the product of their probabilities. So $P = P_1\times P_2=\frac{1}{2}\times\frac{2}{5}=\frac{1}{5}$.

Answer:

$\frac{1}{5}$