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

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In summary, the probability of a winner occurring within the first 10 customers in the bookstore's draw for a $25 book certificate is 9.6%.
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chris_0101
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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
 
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  • #2
chris_0101 said:

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.
 

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

What is the probability of winning a raffle?

The probability of winning a raffle depends on the number of tickets sold and the number of prizes being awarded. For example, if there are 100 tickets sold and 5 prizes, the probability of winning would be 5/100 or 5%.

How can I increase my chances of winning a raffle?

The only way to increase your chances of winning a raffle is to purchase more tickets. However, this does not guarantee a win as the outcome is still based on chance.

What is the difference between probability and odds in a raffle?

Probability refers to the likelihood of an event occurring, while odds refer to the ratio of the probability of an event occurring to the probability of it not occurring. In a raffle, the probability of winning is the number of tickets you have divided by the total number of tickets, while the odds of winning would be the number of tickets you have compared to the number of tickets you do not have.

Can the probability of winning a raffle be calculated?

Yes, the probability of winning a raffle can be calculated by dividing the number of desired outcomes by the total number of possible outcomes. In the case of a raffle, the desired outcome is winning a prize and the total number of possible outcomes is the total number of tickets sold.

What factors can affect the probability of winning a raffle?

The two main factors that can affect the probability of winning a raffle are the number of tickets sold and the number of prizes being awarded. Other factors such as the number of people participating and the number of tickets a person purchases can also impact the probability of winning.

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