Results 1 to 5 of 5

Math Help - Probability that it will rain

  1. #1
    Junior Member
    Joined
    May 2009
    Posts
    68

    Probability that it will rain

    Statistics show that in my city it rains one day out of every four. Also, if it has rained one day, then two times out of three it will rain the next day. If today is fair, the probability that tomorrow will be fair is:
    7/9
    7/12
    8/9
    3/4
    or
    7/8??
    this is all the info im given
    help, please?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Oct 2008
    Posts
    206
    Quote Originally Posted by foreverbrokenpromises View Post
    Statistics show that in my city it rains one day out of every four. Also, if it has rained one day, then two times out of three it will rain the next day. If today is fair, the probability that tomorrow will be fair is:
    7/9
    7/12
    8/9
    3/4
    or
    7/8??
    this is all the info im given
    help, please?
    Hi,
    I think it's 3/4. But I'm not too sure.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    Well I think something is missing.
    I'll use R for rain and F for fair.
    The subscript is which day.
    It seems you're given P(R_1)=1/4 and P(R_2|R_1)=2/3.

    Now P(F_2|F_1)={P(F_1F_2)\over P(F_1)} ={P(F_1F_2)\over 3/4} .

    There are four possibilities so...

    1=P(F_1F_2)+P(R_1F_2)+P(F_1R_2)+P(R_1R_2) .

    P(R_1R_2)= P(R_2|R_1)P(R_1)=(2/3)(1/4) and  P(F_2R_1)=P(F_2|R_1)P(R_1)=(1/3)(1/4).

    So in order to obtain P(F_1F_2) we need P(F_1R_2) .

    It follows that P(F_1R_2)=P(R_2F_1)=P(R_2|F_1)P(F_1)=(?)(3/4) .

    Hence I need P(R_2|F_1) or it's complement probability P(F_2|F_1).
    Last edited by matheagle; May 24th 2009 at 10:18 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by foreverbrokenpromises View Post
    Statistics show that in my city it rains one day out of every four. Also, if it has rained one day, then two times out of three it will rain the next day. If today is fair, the probability that tomorrow will be fair is:
    7/9
    7/12
    8/9
    3/4
    or
    7/8??
    this is all the info im given
    help, please?
    If you try drawing a tree diagram it will quickly become obvious that there is insufficient given information to answer this question.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    May 2009
    Posts
    39
    Quote Originally Posted by matheagle View Post
    Well I think something is missing.
    I'll use R for rain and F for fair.
    The subscript is which day.
    It seems you're given P(R_1)=1/4 and P(R_2|R_1)=2/3.

    Now P(F_2|F_1)={P(F_1F_2)\over P(F_1)} ={P(F_1F_2)\over 3/4} .

    There are four possibilities so...

    1=P(F_1F_2)+P(R_1F_2)+P(F_1R_2)+P(R_1R_2) .

    P(R_1R_2)= P(R_2|R_1)P(R_1)=(2/3)(1/4) and  P(F_2R_1)=P(F_2|R_1)P(R_1)=(1/3)(1/4).

    So in order to obtain P(F_1F_2) we need P(F_1R_2) .

    It follows that P(F_1R_2)=P(R_2F_1)=P(R_2|F_1)P(F_1)=(?)(3/4) .

    Hence I need P(R_2|F_1) or it's complement probability P(F_2|F_1).
    I think we can calculate  P(R_2|F_1) . We have
     P(R_2) = P(F_1)P(R_2|F_1)+P(R_1)P(R_2|R_1)<br />
\rightarrow 1/4 = 3/4 P(R_2|F_1) + 1/4 2/3.
    We obtain  P(R_2|F_1) = 1/9
    So the right answer is 8/9
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Bayes Probability - Rain and Umbrellas
    Posted in the Statistics Forum
    Replies: 1
    Last Post: July 11th 2010, 05:06 PM
  2. Rain Gutter Problem (Optimization)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 15th 2010, 01:28 PM
  3. chance of rain , probability
    Posted in the Statistics Forum
    Replies: 2
    Last Post: July 30th 2009, 01:55 PM
  4. Rain Gutter
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: July 29th 2008, 06:25 AM
  5. Probability of Rain occuring
    Posted in the Statistics Forum
    Replies: 2
    Last Post: May 1st 2007, 08:31 PM

Search Tags


/mathhelpforum @mathhelpforum