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If ten people each have a ten percent chance of winning a prize. What is the probability that at least one of them wins the prize?

Background :

there are 100 prizes to be won, and 1000 people with their names in the hat to win the prize.

Therefore, one person has a ten percent chance of winning... If you can place your name in the hat ten times... what are your odds of winning. (assuming your ten tickets are included within the 1000 total)

How did you figure this out?

Thanks!

Daniel

  • 7
    Find the probability that no one wins, and subtract from 1.2012-06-15
  • 2
    It is important to say whether these events are independent. Otherwise the question may be understood in the way that 10 people are competing and one of them must win.2012-06-15
  • 0
    Depends on the situation. If there are $10$ people and one is picked at random to get the prize, the answer is $1$. But if you assume **independence** $\dots$.2012-06-15
  • 1
    Daniel: So do you have 10 people or 1000 people?2012-06-15
  • 0
    there are 990 total people registered within the competition, and you have the remaining 10 "tickets"2012-06-15
  • 0
    Please clarify in your question (1) how many people are we talking about (2) how many tickets does each person have (3) how many prizes.2012-06-15
  • 0
    each person has one ticket, except for one individual who has ten tickets. Total number of tickets is 1000. There are 100 prizes to be won. Chosen randomly2012-06-15
  • 0
    So there are 991 people?2012-06-15
  • 0
    technically yes... the real question is if I hold 10 of the 1000 tickets... What are my odds of winning at least one of the 100 prizes2012-06-15
  • 0
    @Daniel: In that case it seems Martin's answer is what you are looking for.2012-06-15
  • 0
    10% is the chance that any one of the 1000 wins a prize because there are 100 prizes that everyone has a chance to win (assuming 1000 people with 1 ticket each). But how are the numbers drawn to determine prize winners? (1) Sample with replacement in which case the draws are independent but the probability of winning each time decreases because there are fewer prizes to win or (2) Sample without replacement in which case the successive draws are dependent since the person once drawn no longer has a chance of selection.2012-06-15

2 Answers 2