you pick a card at random, put it back, and then pick another card at random. what is the probability of…

you pick a card at random, put it back, and then pick another 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.

you pick a card at random, put it back, and then pick another 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.

Answer

Explanation:

Step1: Identify prime - numbers and total numbers

The prime numbers among 4, 5, 6, 7, 8, 9 are 5 and 7. So there are 2 prime numbers, and the total number of cards is 6.

Step2: Calculate the probability of the first pick

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 $P_1=\frac{2}{6}=\frac{1}{3}$.

Step3: Calculate the probability of the second pick

Since the card is put back, the situation for the second pick is the same as the first pick. The probability of picking a prime number on the second pick is also $P_2 = \frac{2}{6}=\frac{1}{3}$.

Step4: Calculate the joint - probability

Since the two picks are independent events, the probability of both events occurring is the product of their individual probabilities. So $P = P_1\times P_2=\frac{1}{3}\times\frac{1}{3}=\frac{1}{9}$.

Answer:

$\frac{1}{9}$