What Is the Chance a Bookstore Raffle Winner Is Among the First 10 Customers?

[chris_0101]

Homework Statement

A bookstore has a draw for a $25 book certificate. Each customer draws a ticket from a bowl of 100 tickets. Only one of the tickets is a winning ticket and once the certificate is won, the draw is over. If the tickets are drawn with replacement, what is the probability that the winner is one of the first 10 customers?

Homework Equations

P(win) = 1/100 = 0.01
P(lose) = 1 - P(lose) = 1-0.01 = 0.99

P(winner within first 10 customers) = 1-P(lose)^10

The Attempt at a Solution

P(winner within first 10 customers) = 1-P(lose)^10

P(winner within first 10 customers) =1-(0.99)^10 = 1-0.904 = 0.096 = 9.6%


Therefore, the probability of a winner occurring within the first 10 customers is 9.6%


Just looking for someone to compare answers with and to confirm the answer that I got.

Thanks in advance

 

[Dick]

Homework Statement

A bookstore has a draw for a $25 book certificate. Each customer draws a ticket from a bowl of 100 tickets. Only one of the tickets is a winning ticket and once the certificate is won, the draw is over. If the tickets are drawn with replacement, what is the probability that the winner is one of the first 10 customers?

Homework Equations

P(win) = 1/100 = 0.01
P(lose) = 1 - P(lose) = 1-0.01 = 0.99

P(winner within first 10 customers) = 1-P(lose)^10

The Attempt at a Solution

P(winner within first 10 customers) = 1-P(lose)^10

P(winner within first 10 customers) =1-(0.99)^10 = 1-0.904 = 0.096 = 9.6%


Therefore, the probability of a winner occurring within the first 10 customers is 9.6%


Just looking for someone to compare answers with and to confirm the answer that I got.

Thanks in advance

Seems fine to me.