A number between 0 and 100,000 is chosen. What is the probability of choosing all the...

A number between 0 and 100,000 is chosen. What is the probability of choosing all the digits of the number greater than or equal to 4?

Expert Solution

Solution:
Given in the question
there are 0 to 100000 number are there
Digits greater than or equal to 4 are (4,5,6,7,8,9) which are 6
One digit numbers which are greater than or equal to 4 = 6
Two digits number which has all digits greater than or equal to 4 = 6*6 = 36
Three digits number which has all digits greater than or equal to 4 = 6*6*6 = 216
Four digits number which have all digits greater than or equal to 4 = 6*6*6*6 = 1296
Five digits number which has all digits greater than or equal to 4 = 6*6*6*6*6 = 7776
So the total number of ways to choose a number which have all the digits of the number greater than or equal to 4 = 6+36+216+1296+7776 = 9330
A total number is between 0 and 100000= 99999

probability of choosing all the digits of the number greater than or equal to 4 = 9330/99999 = 0.0933
So there is a 9.33% probability of choosing all the digits of the number greater than or equal to 4.

orchestra answered 2 years ago

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