A 2-digit number will be formed by randomly selecting each digit from the set {2, 3, 9}. What is the probability that the number formed will be 99?

Answer 1

To form the number 99, the first digit must be 9 and the second digit must also be 9:

1. The probability of the first digit being 9 is 1/3
2. The probability of the second digit being 9 is 1/3
3. Since the digit is chosen independently, we multiply the individual probabilities to get the combined probability

Therefore, the probability of both digits being 9 (i.e., forming the number 99) is:

1. P(forming 99) = P(first digit is 9) × P(second digit is 9) = 1/3 × 1/3 = 1/9

Hope this was helpful.

Answer 2

I have worked out the problem in this video for your review. I hope this helps. If you have any additional questions, please let me know. Thank you! Take care

Dr. Christal-Joy Turner

Answer 3

Hey Maria!

How do we determine the probability that the number formed will be 99?

We can think of this "number formation" in two steps (or "events") - picking a first number, and then picking a second number. To form the number 99, in the first step/event, we must pick 9, and in the second step/event, we must pick 9 again.

The probability that we pick a 9 in the first event will be 1/3, as there are 3 possible numbers to choose from and we randomly select one of them - only one of them is nine.

The probability that we pick a 9 in the second event is also 1/3 for the same reasoning, and because the two events are what we call "independent." That is, our outcome for the first event does not change the probability distribution of our second event. There are still only three numbers, and only one of them is 9.

Finally, in probability, there is a simple equation that the probability that event A occurs and that event B occurs is equal to each probability multiplied by one another.

P(A and B) = P(A) x P(B)

In this case, we can think of event "A" as picking a nine as our first number, which has a probability of 1/3: P(A) = 1/3, and event "B" as picking a nine as our second number, which also has a probability of 1/3: P(B) = 1/3.

Therefore, the probability of forming the number 99, or picking both a nine as our first number and our second number, P(A and B) = 1/3 x 1/3 = 1/9.

Hope this helps!