Question

Consider all four-digit numbers that can be made from the digits 0-5

(assume that numbers cannot start with 0
). What is the probability of choosing a random number from this group that is greater than 4000
? Enter a fraction or round your answer to 4
decimal places, if necessary.

Answer 1

The probability of randomly selecting a four-digit number greater than 4000 from the digits 0-5 (where the number does not start with 0) is 0.4000, as there are 432 such numbers out of 1080 possible combinations.

Step-by-step explanation:

To compute the probability of choosing a four-digit number greater than 4000 using the digits 0 through 5, we need to consider the total number of possible four-digit numbers and the subset of those that are greater than 4000.

First, we identify the total number of four-digit combinations possible. Since zero cannot be the first digit, there are 5 choices for the first digit (1-5), 6 choices (0-5) for the second, third, and fourth digits, giving us a total of 5 × 6 × 6 × 6 = 1080 possible combinations.

Next, all four-digit numbers starting with 4 or higher are greater than 4000. The four-digit numbers beginning with '4' have 6 options for each of the remaining three positions, thus generating 6×6×6 = 216 outcomes. Similarly, four-digit numbers starting with 5 will also have 216 possibilities.

So in total, numbers greater than 4000 are 216 (from '4') + 216 (from '5') = 432 outcomes.

The probability is therefore 432 divided by 1080, which simplifies to 2/5 or 0.4.

Therefore, the probability of choosing a random number greater than 4000 is 0.4000.