Results 1 to 3 of 3

Math Help - Basic Probability

  1. #1
    Member
    Joined
    Oct 2008
    Posts
    157

    Basic Probability

    These are three questions on the subject of basic probability. I have answers, could you please check them?

    A bag contains 12 sweets of which 5 are red, 4 are green and 3 are yellow.
    A boy chooses 3 of these sweets at random without replacement. Find the probability that
    (a) he chooses 3 red sweets, [2]
    (b) he chooses no red sweets, [2]
    (c) he chooses 1 sweet of each colour. [3]

    An A-level Mathematics class contains 5 boys and 6 girls. The teacher is told that 3 members of the class can go to a special lecture and she decides to select these 3 members at random. Find the probability that
    (a) 2 boys and 1 girl are selected, [3]
    (b) the 3 members selected are all of the same gender. [4]

    Two unbiased cubical dice are thrown simultaneously. Calculate the probability that
    (a) the score on each die is at least 3, [3]
    (b) the scores on the two dice differ by 3. [3]


    1]
    (a) 5/12 x 4/11 x 3/10 = 60/1320 --> 1/22
    (b) 7/12 x 6/11 x 5/10 = 210/1320 --> 7/44
    (c) 5/12 x 4/11 x 3/10 = 1/22 [there are six different ways of doing this, so 1/22 x 6 = 6/22, or 3/11]


    2]
    (a) 5/11 x 4/10 x 6/9 = 12/99 --> 4/33 [again, there are six different ways so 6 x 4/33 = 24/33]
    (b) 5/11 x 4/10 x 3/9 = 6/99 --> 2/33
    and 6/11 x 5/10 x 4/9 = 4/33
    so 2/33 + 4/33 = 6/33

    3]
    (a) 4/6 x 4/6 = 16/36 --> 4/9
    (b) 6/36 --> 1/6

    Thank you if you can help it is greatly appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member arpitagarwal82's Avatar
    Joined
    Feb 2009
    Posts
    103
    Seems like all answers are correct.
    good job
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,738
    Thanks
    645
    Hello, db5vry!

    Sorry, I don't agree with one of your answers.
    . . But the rest are correct . . . Nice work!


    2) An A-level Mathematics class contains 5 boys and 6 girls.
    The teacher selects 3 members of the class can go to a special lecture.

    Find the probability that:
    . . (a) 2 boys and 1 girl are selected.


    My work:

    (a)\;\frac{5}{11}\times\frac{4}{10}\times\frac{6}{  9} \:=\:\frac{4}{33}

    \text{Again, there are six different ways . . . }\quad{\color{blue}\text{ no}}

    There are only three different ways: . BBG,\:BGB,\:GBB

    The probability is: . \frac{4}{33} \times 3 \:=\:\boxed{\frac{4}{11}}



    Let's solve it a different way . . .

    There are 11 students, 3 are chosen.
    . . There are: . _{11}C_3 \:=\:\frac{11!}{3!\,8!} \:=\:{\color{blue}165} possible outcomes.


    We want 2 of the 5 boys: . _5C_2 \:=\:10 ways.
    We want 1 of the 6 girls: . _6C_1 \:=\:6 ways.
    . . Hence, there are: . 10\cdot6 \:=\:{\color{blue}60} ways to choose 2 boys and a girl.


    Therefore: . P(\text{2 boys, 1 girl}) \:=\:\frac{60}{165} \:=\:\boxed{\frac{4}{11}}

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Re: basic probability
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: March 26th 2010, 08:50 PM
  2. Basic probability #1
    Posted in the Statistics Forum
    Replies: 0
    Last Post: October 2nd 2009, 01:06 PM
  3. Basic probability #2
    Posted in the Statistics Forum
    Replies: 0
    Last Post: October 2nd 2009, 01:06 PM
  4. Basic probability #3
    Posted in the Statistics Forum
    Replies: 0
    Last Post: October 2nd 2009, 01:06 PM
  5. basic probability
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: February 17th 2009, 11:09 PM

Search Tags


/mathhelpforum @mathhelpforum