To solve for the probability of picking a 6 and then an odd number from the given set of cards, we start by determining the total number of cards.
The cards are:
- 6
- 7
- 8
There are 3 cards total.
Step 1: Probability of picking a 6
The probability of picking a 6 as the first card is given by: \[ P(\text{picking a 6}) = \frac{1}{3} \]
Step 2: Probability of picking an odd number after picking a 6
After picking the 6, the remaining cards are:
- 7
- 8
From these, the odd number is 7. There are 2 cards remaining (7 and 8), and only one of them (7) is an odd number.
Thus, the probability of picking an odd number after picking a 6 is: \[ P(\text{picking an odd number | picked a 6}) = \frac{1}{2} \]
Step 3: Combining the probabilities
Now, we multiply the probabilities of the two independent events (picking a 6 first and then picking an odd number): \[ P(\text{6 and then an odd number}) = P(\text{picking a 6}) \times P(\text{picking an odd number | picked a 6}) \] \[ P(\text{6 and then an odd number}) = \frac{1}{3} \times \frac{1}{2} = \frac{1}{6} \]
Thus, the probability of picking a 6 and then picking an odd number is: \[ \boxed{\frac{1}{6}} \]