Question

you pick a card at random. without putting the first card back, you pick a second card at random.
5 6 7 8
what is the probability of picking an odd number and then picking an even number?
write your answer as a fraction or whole number.

Explanation:

Step1: Probability of first odd

There are 4 cards: 5, 6, 7, 8. Odd numbers: 5, 7 (2 cards). So \( P(\text{first odd}) = \frac{2}{4}=\frac{1}{2} \).

Step2: Probability of second even (after first odd)

After picking one odd card, 3 cards left. Even numbers: 6, 8 (2 cards). So \( P(\text{second even}) = \frac{2}{3} \).

Step3: Multiply probabilities

For dependent events, \( P(\text{odd then even}) = P(\text{first odd}) \times P(\text{second even}) = \frac{1}{2} \times \frac{2}{3}=\frac{1}{3} \).

Answer:

\(\frac{1}{3}\)