A is called a palindrome if it reads the same from left and right. For instance,...

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.

Solutions

Expert Solution

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 =

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 =

milcah answered 8 months ago

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