Question

You pick a card at random. Without putting the first card back, you pick a second card at random.

3
4
5
6


What is the probability of picking a 4 and then picking an odd number?

Write your answer as a fraction or whole number.

Answer 1

To calculate the probability of picking a 4 and then picking an odd number from the set of cards {3, 4, 5, 6}, we can follow these steps:

1. **Total Cards**: There are 4 cards in total: 3, 4, 5, and 6.

2. **Probability of Picking a 4**:
- There is one card that is a 4.
- The probability of picking a 4 first is:
\[
P(4) = \frac{1}{4}
\]

3. **After Picking the 4**: Once we pick the 4, we do not put it back. Thus, we are left with the cards: 3, 5, and 6.

4. **Odd Numbers Remaining**: In the remaining cards, 3 and 5 are odd numbers.
- So there are 2 odd numbers left (3 and 5) out of 3 remaining cards.

5. **Probability of Picking an Odd Number After Picking a 4**:
- The probability of picking an odd number after picking a 4 is:
\[
P(\text{odd after 4}) = \frac{2}{3}
\]

6. **Combined Probability of Both Events**:
- Now, we multiply the probabilities of both events occurring:
\[
P(4 \text{ then odd}) = P(4) \times P(\text{odd after 4}) = \frac{1}{4} \times \frac{2}{3} = \frac{2}{12} = \frac{1}{6}
\]

Thus, the probability of picking a 4 and then an odd number is \(\frac{1}{6}\).