Results 1 to 2 of 2

Math Help - Law of Total Probability

  1. #1
    Junior Member
    Joined
    Oct 2008
    From
    Dallas, TX
    Posts
    71

    Law of Total Probability

    A small brewery has three bottling machines. Machine A produces 40% of all the bottles, machines B and C produce 30% each. Five percent of bottles filled by A, four percent of bottles filled by B, and three percent of bottles filled by C are rejected for some reason.

    (a) If a bottle is filled by A or B, what is the probability that it is rejected?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Hello aaronrj
    Quote Originally Posted by aaronrj View Post
    A small brewery has three bottling machines. Machine A produces 40% of all the bottles, machines B and C produce 30% each. Five percent of bottles filled by A, four percent of bottles filled by B, and three percent of bottles filled by C are rejected for some reason.

    (a) If a bottle is filled by A or B, what is the probability that it is rejected?
    Consider 100 bottles produced by all three machines. Of these, A produces 40, B and C 30 each. So in 70 bottles produced by A and B, 40 will come from A and 30 from B.

    So, given that the bottles come from A and B, the probability that a given bottle is from A is \tfrac47, and from B \tfrac37. Given that the probabilities that they are rejected are 0.05 and 0.04 respectively, the probability that a bottle chosen at random is rejected is:
    \tfrac47\times 0.05 + \tfrac37\times 0.04 = 0.0457
    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. probability law of total porbab, problem.
    Posted in the Statistics Forum
    Replies: 1
    Last Post: November 21st 2010, 02:21 PM
  2. Conditional Probability using the Law of Total Probability
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 7th 2010, 03:01 AM
  3. Law of Total Probability
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: April 21st 2010, 04:47 PM
  4. law of total probability
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: January 30th 2010, 01:47 AM
  5. Proof of total probability theorem
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: December 23rd 2009, 12:25 AM

Search Tags


/mathhelpforum @mathhelpforum