Question

All possible 3-digit numbers made with only the digits 1 and 2 are written on separate pieces of paper. Without looking, Liam takes one piece. What is the probability that the number on the paper will use just one digit?

Answer 1

The probability that a randomly selected three-digit number made with only the digits 1 and 2 contains just one digit is 1/4 (or 0.25).

Step-by-step explanation:

The question asks to calculate the probability that a three-digit number comprised only of the digits 1 and 2 will contain just one digit when selected at random. To solve this, we recognize that there are two possible numbers that satisfy this condition: 111 and 222. Since the numbers are all possible combinations of 1 and 2 in a three-digit format, there are 23 (or 8) total possible numbers (111, 112, 121, 122, 211, 212, 221, and 222). Therefore, the probability of randomly selecting a number with just one digit is the number of single digit numbers (2) divided by the total possible numbers (8), resulting in a probability of 2/8, which simplifies to 1/4 or 0.25.