Results 1 to 2 of 2

Math Help - Advanced Probability Help!!!

  1. #1
    Junior Member
    Joined
    Apr 2008
    Posts
    40

    Advanced Probability Help!!!

    Peter was given n one-dollar scratch tickets, each winning:

    $2 with probability 1/8
    $10 ------------- 1/100
    $1000 ----------- 1/10,000
    $20000 ---------- 1/1,000,000

    1. Let An , where n is a subscript, be the event that Peter wins on at least one of the n tickets he was given. Compute Pr(A8).

    2. What is the minimum number of n tickets Peter should be given to ensure that Pr(An)>0.5?

    3. Compute the expected value of Peter's winnings when n=8.

    How do I do these questions?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by maibs89 View Post
    Peter was given n one-dollar scratch tickets, each winning:

    $2 with probability 1/8
    $10 ------------- 1/100
    $1000 ----------- 1/10,000
    $20000 ---------- 1/1,000,000

    1. Let An , where n is a subscript, be the event that Peter wins on at least one of the n tickets he was given. Compute Pr(A8).

    2. What is the minimum number of n tickets Peter should be given to ensure that Pr(An)>0.5?

    3. Compute the expected value of Peter's winnings when n=8.

    How do I do these questions?
    The probability that a single ticket wins a prize is p = \frac{1}{8} + \frac{1}{100} + \frac{1}{10,000} + \frac{1}{1,000,000} = ......

    Let X be the random variable number of tickets that win a prize.

    Then X ~ Binomial(n, p).


    1. n = 8: Find Pr(X > 0) = 1 - Pr(X = 0).


    2. Require Pr(X > 0) > 0.5 => 1 - Pr(X = 0) > 0.5 => Pr(X = 0) < 0.5.

    So solve {n \choose 0} p^0 (1 - p)^n < 0.5 \Rightarrow (1 - p)^n < 0.5.


    3. Let Y be the random variable amount of money won with 1 ticket.

    Then E(Y) = 2 \left( \frac{1}{8}\right) + 10 \left( \frac{1}{100} \right) + 1,000 \left( \frac{1}{10,000} \right) + 20,000 \left( \frac{1}{1,000,000}\right) = ......

    The expected amount of money won with 8 tickets is 8 E(Y) = ......
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simple probability or more advanced technique?
    Posted in the Statistics Forum
    Replies: 2
    Last Post: October 4th 2011, 08:56 PM
  2. Advanced Draw Probability issue
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: January 7th 2010, 01:41 PM
  3. Advanced Probability Question
    Posted in the Statistics Forum
    Replies: 6
    Last Post: October 6th 2009, 06:50 AM
  4. Advanced Blackjack Probability
    Posted in the Statistics Forum
    Replies: 1
    Last Post: February 2nd 2009, 03:15 PM
  5. Advanced Probability, urgent for tomorrow's test
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: March 4th 2008, 03:07 PM

Search Tags


/mathhelpforum @mathhelpforum