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 9 and then picking a 9? write your answer 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 9 and then picking a 9? write your answer as a fraction or whole number.

Answer

Explanation:

Step1: Calculate probability of first pick

There are 3 cards and 1 card with number 9. So the probability of picking a 9 on the first pick is $\frac{1}{3}$.

Step2: Calculate probability of second pick

Since the card is put - back, there are still 3 cards and 1 card with number 9. So the probability of picking a 9 on the second pick is $\frac{1}{3}$.

Step3: Calculate combined probability

For independent events, the combined probability is the product of the individual probabilities. So $P=\frac{1}{3}\times\frac{1}{3}=\frac{1}{9}$.

Answer:

$\frac{1}{9}$