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(A) The total number of pages is $100$. The page numbers are from $1$ to $100$.We need to find the numbers between $1$ and $100$ such that the sum of

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$\frac{2}{25}$

Vedclass · Answer

(A) The total number of pages is $100$. The page numbers are from $1$ to $100$.We need to find the numbers between $1$ and $100$ such that the sum of their digits is $11$.For a two-digit number $xy$,the sum of digits is $x + y = 11$,where $1 \le x \le 9$ and $0 \le y \le 9$.The possible pairs $(x, y)$ are $(2, 9), (3, 8), (4, 7), (5, 6), (6, 5), (7, 4), (8, 3), (9, 2)$.These correspond to the page numbers: $29, 38, 47, 56, 65, 74, 83, 92$.There are $8$ such numbers.For the number $100$,the sum of digits is $1 + 0 + 0 = 1 
eq 11$.Thus,the number of favourable outcomes is $8$.The total number of outcomes is $100$.The probability is $\frac{8}{100} = \frac{2}{25}$.

From a book containing $100$ pages,one page is selected randomly. The probability that the sum of the digits of the page number of the selected page is $11$,is

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