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: Determine prime numbers

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

Step2: Calculate probability of first pick

Probability of picking a prime number first is \(P_1=\frac{2}{5}\).

Step3: Calculate probability of second pick

After picking one prime - numbered card (without replacement), there is 1 prime number left out of 4 cards. So probability of picking a prime number second is \(P_2 = \frac{1}{4}\).

Step4: Calculate combined probability

Since these are dependent events, use the formula \(P = P_1\times P_2\). Substitute \(P_1=\frac{2}{5}\) and \(P_2=\frac{1}{4}\), we get \(P=\frac{2}{5}\times\frac{1}{4}=\frac{2\times1}{5\times4}=\frac{2}{20}=\frac{1}{10}\).

Answer:

\(\frac{1}{10}\)