Results 1 to 2 of 2

Math Help - probability

  1. #1
    Gad
    Gad is offline
    Newbie
    Joined
    Jun 2012
    From
    Ghana
    Posts
    1

    probability

    Police plan to enforce speed limits by using radar traps at different locations within the Kumasi Metropolis. The radar traps at each of the locations L1, L2, L3 and L4 are operated 40%, 30%, 20% and 30% of the time, and if a person who is speeding on his way to work has probabilities 0.2, 0.1, 0.5, and 0.2 respectively, of passing through these locations:

    1. what is the probability that he will receive a speeding ticket?
    \2. if a person received a speeding ticket on his way to work, what is the probability that he passed the trap located at L2
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,298
    Thanks
    1276

    Re: probability

    Quote Originally Posted by Gad View Post
    Police plan to enforce speed limits by using radar traps at different locations within the Kumasi Metropolis. The radar traps at each of the locations L1, L2, L3 and L4 are operated 40%, 30%, 20% and 30% of the time, and if a person who is speeding on his way to work has probabilities 0.2, 0.1, 0.5, and 0.2 respectively, of passing through these locations:

    1. what is the probability that he will receive a speeding ticket?
    In order to get a ticket you would have to pass through location L_1, which has probability of .2, when the radar "trap" was operating, which has probability .4, so that both happening (passing through L_2 while it is operating) has probability (.2)(.4)= .08 OR pass through location L_2, which has probability .1, when the radar "trap" is operating, which has probability .3, so that both happening has probability (.1)(.3)= .03, or ..., etc. The total probability of all those "ors" is the sum of each probability.

    2. if a person received a speeding ticket on his way to work, what is the probability that he passed the trap located at L2
    I like to handle these kids of problems "en masse". That is, suppose the person drives to work 100 times. In those 100 times, he will pass L_1 .4(100)= 40 times and will get a ticket .2(40)= 8 times. He will pass L_2 .3(100)= 30 times and will get a ticket .1(30)= 3 times. He will pass L_3 .2(100)= 20 times and will get a ticket .5(20)= 10 times. He will pass L_4 .3(100)= 30 times and will get a ticket .2(30)= 6 times.

    In total, then, he got 8+ 3+ 10+ 6= 27 tickets (which also gives an answer to (1)), 3 of them at L_2. Given that he got a ticket, the probability it was from L_2 is frac{3}{27}= \frac{1}{9}.

    (Let's hope that with that many speeding tickets he loses his license and stays off the road!)
    Last edited by HallsofIvy; June 25th 2012 at 07:12 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 10
    Last Post: January 21st 2011, 11:47 AM
  2. Replies: 3
    Last Post: May 29th 2010, 07:29 AM
  3. Replies: 1
    Last Post: February 18th 2010, 01:54 AM
  4. Replies: 0
    Last Post: January 20th 2010, 06:04 AM
  5. Replies: 3
    Last Post: December 15th 2009, 06:30 AM

Search Tags


/mathhelpforum @mathhelpforum