A book contains 1000 pages. A page is chosen at random. The...

A book contains 1000 pages. A page is chosen at random. The probability that the sum of the digits of the marked number on the page is equal to 9 , is

Options

A $\frac{23}{500}$
B $\frac{11}{200}$
C $\frac{7}{100}$
DNone of these

Correct answer

B. $\frac{11}{200}$

Step-by-step solution

n(S)=

Total number of ways

=1000

The favourable cases that the sum of the digits of the marked number on the page is equal to 9 are one digit number or two digits numbers or three digits numbers, if three digit number is

a b c

. Then,

a+b+c=9 ; 0 \leq a, b, c \leq 9

\therefore n(E)=

Number of favourable ways = Number of solutions of the equation

=\binom{9+3-1}{3-1}={ }^{11} C_2=55\therefore

Required probability

=\frac{n(E)}{n(S)}=\frac{55}{1000}=\frac{11}{200}

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