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: 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.

Step2: Calculate first - pick probability

The probability of picking a prime number on the first pick is $P_1=\frac{2}{5}$.

Step3: Calculate second - pick probability

Since we don't put the first card back, for the second pick, there are 4 cards left. If the first card was prime, then there is 1 prime number left among the 4 cards. 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 combined probability

By the multiplication rule for independent - events (in the context of non - replacement probability), the probability of both events happening is $P = P_1\times P_2=\frac{2}{5}\times\frac{1}{4}=\frac{2}{20}=\frac{1}{10}$.

Answer:

$\frac{1}{10}$