Question

Consider all of the four-digit numbers that can be formed using the digits 1, 2, 3, and 4 when no digit is used twice. What is the probability that one of these numbers, when chosen at random, is between 2000 and 3000?
A. 20%

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B. 25%

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C. 33 %

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D. 50%
Please help I’ll give brainliest

Answer 1

Answer:

Option B

Step-by-step explanation:

Given: all the four-digit numbers are formed using the digits 1, 2, 3, and 4 such that no digit is used twice

To find: probability that number chosen lies between 2000 and 3000

Solution:

Probability refers to chances of occurring of some event.

Total number of numbers formed using digits 1, 2, 3, and 4 = $4\times 3\times 2\times 1=24$

Numbers between 2000 and 3000 start with 2. So, first digit is fixed as 2. For remaining three digits, possibilities are 4, 3, 1

So, total number of numbers lie between 2000 and 3000 = $3\times 2\times 1=6$

Probability that number chosen lies between 2000 and 3000 = total number of numbers lie between 2000 and 3000/Total number of numbers formed using digits 1, 2, 3, and 4 = 6/24 = 1/4

In percentage form, Probability that number chosen lies between 2000 and 3000 = $\frac{1}{4}(100)=25\%$