you pick a card at random. without putting the first card back, you pick a second card at random. 5 6 7 8 9…

Explanation:

Step1: Identify prime - numbers

The prime numbers among 5, 6, 7, 8, 9 are 5 and 7. So there are 2 prime numbers out of 5 numbers initially.

Step2: Calculate the first - pick probability

The probability of picking a prime number on the first pick is the number of prime numbers divided by the total number of numbers. So (P_1=\frac{2}{5}).

Step3: Calculate the second - pick probability

Since we do not put the first card back, there are 4 numbers left. If the first number was prime, then there is 1 prime number left. So the probability of picking a prime number on the second pick given that the first pick was prime is (P_2 = \frac{1}{4}).

Step4: Calculate the combined probability

The probability of both events happening is the product of the probabilities of each event. So (P = P_1\times P_2=\frac{2}{5}\times\frac{1}{4}=\frac{2}{20}=\frac{1}{10}).

Answer:

(\frac{1}{10})