Respuesta :
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 = [tex]4\times 3\times 2\times 1=24[/tex]
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 = [tex]3\times 2\times 1=6[/tex]
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 = [tex]\frac{1}{4}(100)=25\%[/tex]
Probability that a four digit number formed from 1,2,3,4 is between 2000 & 3000 = 25%
Calculation of Probability
Total number of four digit numbers that can be formed by digits 1,2,3,4 (without repetition)
Possible outcomes for first digit = 4
Possible outcomes for second digit = 3
Possible outcomes for third digit = 2
Possible outcomes for fourth digit = 1
So, total ways in which mentioned 4 digit number can be formed = 4 x 3 x 2 x 1 = 24 ways
When number is between 2000 & 3000, it starts from digit 2
So, possible outcome for first digit = only 1 ( ie digit 2)
Possible outcomes for second digit = 3
Possible outcomes for third digit = 2
Possible outcomes for fourth digit = 1
So, total ways in which 4 digit number starting from digit '2' can be formed = 1 x 3 x 2 x 1 = 6 ways
Probability = Favourable outcomes / Total outcomes
6 / 24 = 0.25 = 25%
To learn more about Probability, refer https://brainly.com/question/743546?referrer=searchResults
