Question

you pick a card at random, put it back, and then pick another card at random.
6 7 8 9
what is the probability of picking a 9 and then picking a prime number?
simplify your answer and write it as a fraction or whole number.

Explanation:

Step1: Calculate the probability of picking a 9

There are 4 cards in total. The probability of picking a 9 is \(P(9)=\frac{1}{4}\) since there is 1 card with the number 9.

Step2: Calculate the probability of picking a prime number

The prime number among 6, 7, 8, 9 is 7. So the probability of picking a prime number is \(P(\text{prime})=\frac{1}{4}\) as there is 1 prime - numbered card out of 4.

Step3: Use the multiplication rule for independent events

Since the two picks are independent events (because we put the first card back), the probability of both events occurring is \(P = P(9)\times P(\text{prime})\).
Substitute the values: \(P=\frac{1}{4}\times\frac{1}{4}\)

$$P=\frac{1\times1}{4\times4}=\frac{1}{16}$$

Answer:

\(\frac{1}{16}\)