In: Math
A is called a palindrome if it reads the same from left and right. For instance, 13631 is a palindrome, while 435734 is not. A 6-digit number n is randomly chosen. Find the probability of the event that
(a) n is a palindrome.
(b) n is odd and a palindrome.
(c) n is even and a palindrome.
There are total 999,999 six digits number .
In that numbers Total pallindrome numbers are :
Now let ABCDEF be the six digit number ,Since ABCDEF Is pallindrome number ,Therefore A=F ,B=E & C=D
A can be any letter from 1 to 9 .
I.e. A has 9 possible digits . In similar way B has 10 choices And C has 10 choices .(B and C taking value 0 also )
Therefore , Total possible 6 digit pallindrome numbers are 9*10*10 = 900
(a) Probability that n is palindrome =
(b) Probability that n is odd and n is pallindrome :
Odd number means the number which is not divisible by 2 that means the number has digit 1,3,5,7,9 at the unit place .
Since number is pallindrome the choices of first digit is also 1,3,5,7,9.
I.e Total possible odd 6 digit pallindrome numbers are 5*10*10 = 500
Probability that n is odd and n is pallindrome =
(c) Probability that n is even and n is pallindrome :
Odd number means the number which is divisible by 2 that means the number has digit 0,2,4,6,8 at the unit place .
But 0 is not possible because if we take 0 then number will of 5 digits
Since number is pallindrome the choices of first digit is also 2,4,6,8.
I.e Total possible odd 6 digit pallindrome numbers are 4*10*10 = 400
Probability that n is even and n is pallindrome =