A lottery company creates lottery tickets with numbers from 00 to 99. The winning number is randomly chosen by two people. Sok buys a lottery ticket with a number that is a multiple of 9. Find the probability that Sok wins the lottery.

1. Problem Description

A lottery company creates lottery tickets with numbers from 00 to

9

9. The winning number is randomly chosen by two people. Sok buys a lottery ticket with a number that is a multiple of

9. Find the probability that Sok wins the lottery.

2. Solution Steps

The lottery tickets are numbered from 00 to

9

9. This means there are $100$ possible lottery ticket numbers.

The numbers that are multiples of $9$ are $0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99$.

So there are $12$ numbers which are multiples of $9$ between $00$ and $99$.

The probability that Sok wins the lottery is the number of favorable outcomes divided by the total number of possible outcomes.

Since Sok buys a ticket which is a multiple of $9$, the number of favorable outcomes is

1.

However, the problem asks for the probability that Sok *wins* given that he has bought a ticket which is a multiple of

9. We are given that Sok's ticket number is a multiple of 9, and we want to find the probability that the winning number is also a multiple of 9, and is Sok's number.

The total number of possible outcomes is 100, since the lottery tickets are numbered from 00 to

9

9. Sok has purchased a ticket with a number which is a multiple of

9. There are 12 such numbers: $0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99$.

The probability that the winning number is one of these numbers is $\frac{12}{100}$.

If Sok buys one such ticket, say $9$, then the probability that Sok's ticket is the winning ticket is $\frac{1}{100}$.

Since Sok's ticket number is a multiple of 9, the probability that Sok wins is $\frac{1}{100}$.

Alternatively, we are looking for the probability that the winning number is a multiple of 9, given that Sok's ticket is a multiple of

9.

The question is asking for the probability that Sok wins.

The number of lottery tickets is 100, numbered from 00 to

9

9. Sok buys one ticket.

The probability that Sok wins is $\frac{1}{100} = 0.01$.

3. Final Answer

1/100