Question

A license plate is 3 capital letters of english alphabets and 3 digits.If all cases are equally likely possibility that the plate has either a letter or digit palindrome or both is:

• A. 9/65
• B. 8/65
• C. 7/52
• D. 13/51

Answer 1

The correct option is C

7/52

P(all letter palindrome)=$\frac{{26}^2}{{26}^3}$=(L1,L2,L1)=P(A)

P(All digit palindrome)=$\frac{{10}^2}{{10}^3}$=(D1,D2,D1)=P(B)

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P\left(AintersectionB\right)$

$P(A\cup B)=\frac{1}{26}+\frac{1}{10}-\frac{1}{260}=\frac{7}{52}$