Question

you pick a card at random. without putting the first card back, you pick a second card at random. what is the probability of picking a prime number and then picking a prime number? simplify your answer and write it as a fraction or whole number.

Explanation:

Step1: Count prime - numbered cards and total cards

There are 2 prime - numbered cards (5 and 7) out of 6 total cards initially. The probability of picking a prime - numbered card on the first draw is $\frac{2}{6}=\frac{1}{3}$.

Step2: Calculate probability of second draw

After the first draw without replacement, there are 5 cards left. If the first card was prime, then there is 1 prime - numbered card left. So the probability of picking a prime - numbered card on the second draw, given that the first card was prime, is $\frac{1}{5}$.

Step3: Use multiplication rule for dependent events

The probability of both events (picking a prime first and then a prime second) is the product of the probabilities of each event. So $P=\frac{1}{3}\times\frac{1}{5}=\frac{1}{15}$.

Answer:

$\frac{1}{15}$