Question

you pick a card at random. without putting the first card back, you pick a second card at random.
2 3 4 5
6 7 8 9
what is the probability of picking a prime number and then picking a prime number?
write your answer as a fraction or whole number.

Explanation:

Step1: Identify prime numbers

Prime numbers in the set {2, 3, 4, 5, 6, 7, 8, 9} are 2, 3, 5, 7. So there are 4 prime numbers. Total cards: 8.
Probability of first prime: $\frac{4}{8}=\frac{1}{2}$.

Step2: Probability of second prime (without replacement)

After picking one prime, remaining primes: 3, total remaining cards: 7.
Probability of second prime: $\frac{3}{7}$.

Step3: Multiply probabilities (independent events in sequence)

Probability = $\frac{1}{2} \times \frac{3}{7} = \frac{3}{14}$.

Answer:

$\frac{3}{14}$