Results 1 to 5 of 5
Like Tree1Thanks
  • 1 Post By MaxJasper

Math Help - Probability selection with replacement (balls in an urn)

  1. #1
    Newbie
    Joined
    Sep 2012
    From
    United States
    Posts
    3

    Probability selection with replacement (balls in an urn)

    Hello,

    I have a question regarding this subject. If we have replacement, technically the odds of pulling one colored ball remains he same form draw to draw, thus they're independent events, right? Here is a specific example.

    There is an urn with 80 blue balls, 60 red balls, and 60 green balls.

    If I draw from this urn twice, with replacement, what is the probability that at least one ball is blue given that at least one ball is either green or red?

    I go back and forth on this... since it is replacement, part of me says that there will always be a 40% chance that any ball pulled is blue. However, if we have the scenario where there is two balls, and we know that for sure one of the balls chosen will be red or green (60%), would I multiply 80/200 * 120/200?


    What is the probability that at least one ball is blue given that the SECOND ball is either green or red?


    Does it matter that we know that the second ball is either green or red or is this question to be approached the same way we would answer the reverse - what is the probability that at least one ball is blue given that the FIRST ball is either green or red.... same question? My gut says that this is the same answer as above.

    Any insight that could help me get this to click would be greatly appreciated. Thank You.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member MaxJasper's Avatar
    Joined
    Aug 2012
    From
    Canada
    Posts
    482
    Thanks
    54

    Lightbulb Re: Probability selection with replacement (balls in an urn)

    Quote Originally Posted by JGWENTWORTH View Post

    There is an urn with 80 blue balls, 60 red balls, and 60 green balls. If I draw from this urn twice, with replacement, what is the probability that at least one ball is blue given that at least one ball is either green or red?
    Your restrictions give only two drawing possibilities: \{g,b\} and \{r,b\}

    Combined probabilities would be:

    P\{g,b\}+P\{r,b\}=P(g=1|60,200)*P(b=1|80,200)+P(r=  1|60,200)*P(b=1|80,200)=\frac{6}{25}
    Thanks from JGWENTWORTH
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2012
    From
    United States
    Posts
    3

    Re: Probability selection with replacement (balls in an urn)

    Thanks MaxJasper, in short on this one we're 4/10*6/10. This was the approach that I took. If we had an urn with 20 total balls, 10 yellow and 10 orange, in it and selected 2 balls with replacement, what is the probability that at least one of the balls is orange given that at least one is yellow? Would I take the same approach here? 1/2 * 1/2 = 1/4 ? I see 2/3 being a possibility too as we're looking at OO, YY, OY, YO as possibilities and since we know at least one is yellow, that eliminates OO, leaving us 3 options, YY, OY, and YO... and if at least one of the balls is orange, we have 2 of these 3 possibilities remaining... am I over thinking this? Thanks again!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member MaxJasper's Avatar
    Joined
    Aug 2012
    From
    Canada
    Posts
    482
    Thanks
    54

    Re: Probability selection with replacement (balls in an urn)

    Again your restrictions specified as "at least" results in only {Y,O} and remember that {Y,O}={O,Y} and so you end up with only {Y,O} no matter what order of drawing the balls. You don't have combinations: {O,O}, {Y,Y} because "at least" is violated!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2012
    From
    United States
    Posts
    3

    Re: Probability selection with replacement (balls in an urn)

    This being said, the solution for the second question would be 1/2*1/2=0.25 ?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: March 10th 2012, 04:48 PM
  2. Drawing balls randomly with replacement
    Posted in the Statistics Forum
    Replies: 2
    Last Post: November 14th 2011, 12:59 PM
  3. Random selection without replacement.
    Posted in the Statistics Forum
    Replies: 2
    Last Post: September 2nd 2011, 05:47 PM
  4. Drawing Balls from Urns with Replacement
    Posted in the Statistics Forum
    Replies: 1
    Last Post: August 24th 2011, 10:03 AM
  5. probability of selection
    Posted in the Statistics Forum
    Replies: 4
    Last Post: February 1st 2010, 10:49 AM

Search Tags


/mathhelpforum @mathhelpforum