Question

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

3
4
5
6
7


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

Write your answer as a percentage.

%

Answer 1

To find the probability of picking an odd number first and then an even number from the given set of cards (3, 4, 5, 6, 7), we can follow these steps:

1. Identify the odd and even numbers in the set:
- Odd numbers: 3, 5, 7 (total of 3 odd numbers)
- Even numbers: 4, 6 (total of 2 even numbers)

2. Calculate the probability of picking an odd number first:
- There are 5 cards in total.
- The probability of picking an odd number first is:
\[
P(\text{odd first}) = \frac{3}{5}
\]

3. After picking an odd number, one card is removed, leaving 4 cards remaining. The number of even numbers remains the same (2 even numbers).

4. Calculate the probability of picking an even number after picking an odd number:
- The probability of picking an even number second is:
\[
P(\text{even second | odd first}) = \frac{2}{4} = \frac{1}{2}
\]

5. Now, calculate the combined probability of both events occurring (picking an odd number first followed by an even number):
\[
P(\text{odd first and even second}) = P(\text{odd first}) \times P(\text{even second | odd first}) = \frac{3}{5} \times \frac{1}{2} = \frac{3}{10}
\]

6. Convert the probability to a percentage:
\[
\frac{3}{10} = 0.3
\]
\[
0.3 \times 100 = 30\%
\]

Thus, the probability of picking an odd number and then picking an even number is **30%**.