Select the correct answer.

A community group sells 2,000 tickets for its raffle. The grand prize is a car. Neil and 9 of his friends buy 10 tickets each. When the winning ticket number is announced, it is found to belong to Neil's group. Given this information, what is the probability that the ticket belongs to Neil?

A. [tex]\frac{1}{4}[/tex]
B. [tex]\frac{1}{2000}[/tex]
C. [tex]\frac{1}{5}[/tex]
D. [tex]\frac{1}{10}[/tex]



Answer :

Let's go through the problem step by step to find the correct answer.

1. Total Tickets Sold:
[tex]\[ \text{Total tickets} = 2000 \][/tex]

2. Neil's Group Tickets:
Neil and 9 of his friends each bought 10 tickets.
[tex]\[ \text{Total tickets bought by Neil's group} = 10 \times 10 = 100 \][/tex]

3. Probability that the Winning Ticket Belongs to Neil's Group:
We are given that the winning ticket indeed belongs to Neil's group. Therefore, the probability calculation involves consideration within Neil's group only.

4. Total Tickets within Neil's Group:
Each person, including Neil, buys 10 tickets. Thus, there are 10 people:
[tex]\[ \text{Total tickets in Neil's group} = 10 \text{ tickets per person} \times 10 \text{ people} = 100 \][/tex]

5. Probability that the Winning Ticket Belongs to Neil:
Within Neil's group, Neil also holds 10 tickets out of the 100 tickets.
[tex]\[ \text{Probability that Neil's tickets win} = \frac{\text{Number of Neil's tickets}}{\text{Total tickets in Neil's group}} = \frac{10}{100} = \frac{1}{10} \][/tex]

Hence, the correct answer is:
\[ \boxed{\frac{1}{10}}