Question

you pick a card at random. without putting the first card back, you pick a second card at random.
1 2 3
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 among 1, 2, 3: 2, 3 (1 is not prime). So there are 2 prime numbers out of 3 total. Probability first pick is prime: $\frac{2}{3}$.

Step2: Probability second pick (without replacement)

After picking one prime, 1 prime left and 2 total cards. Probability second pick is prime: $\frac{1}{2}$.

Step3: Multiply probabilities

Probability of both events: $\frac{2}{3} \times \frac{1}{2} = \frac{1}{3}$.

Answer:

$\frac{1}{3}$