Question

In a password, there are 6 characters. The characters can be any 10 digits or 26 lowercase letters. Repetition is allowed, order does not matter. Calculate the probability that the first character is a digit

Answer 1

Solution:
Given in the question
Total no. of digits = 10, i.e. 0,1,2,3,4,5,6,7,8,9
No. of lowercase letters = 26, a,b,c,d,e,f,g,hi,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z
So total characters= 26+10 = 36
We need to make a password which have 6 characters
First character is a digit which can be choose from 10 ways
Second character can be digit or letters and repetition is allowed so this can be choose in 36 ways
Third character can be digit or letters and repetition is allowed so this can be choose in 36 ways
Fourth character can be digit or letters and repetition is allowed so this can be choose in 36 ways
Fifth character can be digit or letters and repetition is allowed so this can be choose in 36 ways
Sixth character can be digit or letters and repetition is allowed so this can be choose in 36 ways
So total no. of ways to make 6 characters password that the first character is a digit = 10*36*36*36*36*36
and total no. of ways to make 6 character password from 10 digits or 26 lowercase letters = 36*36*36*36*36*36
Probability that the first character is a digit = total no. of ways to make 6 characters password that the first character is a digit/total no. of ways to make 6 character password from 10 digits or 26 lowercase letters = (10*36*36*36*36*36)/(36*36*36*36*36*36) = 10/36 = 0.2778
So there is 27.78% probability that the first character is a digit.