Results 1 to 2 of 2

Math Help - Probability Problem (tree diagram)

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    12

    Probability Problem (tree diagram)

    A couple has three babies.
    a. what are the chances 3 are girls?
    b. what are the chances there will be boy,girl,boy?

    http://i49.tinypic.com/2isyo0.jpg

    ^ is tree diagram


    a.

    n(S)=(2^3) = 8
    n(A)=7?

    P(A)=7/8


    b. n(S)=(2^3)=8
    n(A)=3

    P(A)=3/8




    Also.. another from the textbook:

    Suppose your school's basketball team is playing a four-game series against another school. So far this season, each team has won three of the six games in which they faced each other.

    a) Determine the probability of your school winning exactly two games. (use your tree diagram)

    I'm not sure how to do this.

    n(S)=(2^4)=16
    n(A) = ?

    P(A) = n(A)/16

    How to find n(A) here i'm not sure
    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
    Thanks
    1
    Hello Johnboe
    Quote Originally Posted by Johnboe View Post
    A couple has three babies.
    a. what are the chances 3 are girls?
    b. what are the chances there will be boy,girl,boy?

    http://i49.tinypic.com/2isyo0.jpg

    ^ is tree diagram


    a.

    n(S)=(2^3) = 8
    n(A)=7?

    P(A)=7/8


    b. n(S)=(2^3)=8
    n(A)=3

    P(A)=3/8




    Also.. another from the textbook:

    Suppose your school's basketball team is playing a four-game series against another school. So far this season, each team has won three of the six games in which they faced each other.

    a) Determine the probability of your school winning exactly two games. (use your tree diagram)

    I'm not sure how to do this.

    n(S)=(2^4)=16
    n(A) = ?

    P(A) = n(A)/16

    How to find n(A) here i'm not sure
    Question 1

    Your tree diagram is correct. But in (a) only one of the 8 possible outcomes is favourable ( 3 girls). So the probability of this is \tfrac18.

    In (b), if the question means B, G, B in that order, then, again, only one outcome is favourable. So again the probability is \tfrac18. However, if the question means "What is the probability that they have 2 boys and a girl?", then your answer \tfrac38 is correct.

    Question 2

    Of course, in reality, the results of previous games cannot be used with any degree of certainty to predict future results. However, if we assume that, based on past form, the probability that your team wins a particular game is \tfrac12, then we can draw a tree diagram to represent the 16 possible sets of outcomes of four games, with each outcome equally likely. (Just extend the tree diagram you had in Question 1 to another level.)

    You'll find that, of the 16 possible paths through the tree, 6 of them result in 2 wins and 2 losses. So the probability of exactly 2 wins is \tfrac{6}{16}= \tfrac38.

    (If you're not sure what these 6 possible paths are, here they are: WWLL, WLWL, WLLW, LWWL, LWLW, LLWW.)

    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Probability Tree Diagram Problem
    Posted in the Statistics Forum
    Replies: 3
    Last Post: February 27th 2010, 09:50 PM
  2. Probability: tree diagram
    Posted in the Statistics Forum
    Replies: 1
    Last Post: December 9th 2009, 05:38 AM
  3. Probability tree diagram
    Posted in the Statistics Forum
    Replies: 5
    Last Post: May 2nd 2009, 01:08 PM
  4. Tree diagram, probability.
    Posted in the Statistics Forum
    Replies: 1
    Last Post: April 5th 2009, 02:38 PM
  5. [Probability] – A tree diagram problem
    Posted in the Statistics Forum
    Replies: 2
    Last Post: October 11th 2008, 05:15 PM

Search Tags


/mathhelpforum @mathhelpforum