Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By ebaines

Math Help - Probability

  1. #1
    Newbie
    Joined
    Jul 2014
    From
    sacramento
    Posts
    2

    Probability

    If a seed is planted, it has a 90% chance of growing into a healthy plant.

    If 9 seeds are planted, what is the probability that exactly 2 don't grow?


    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor ebaines's Avatar
    Joined
    Jun 2008
    From
    Illinois
    Posts
    1,091
    Thanks
    315

    Re: Probability

    For exactly 2 plants to not grow, that means 7 do grow. The probability of an individual plant growing is p=0.9. Conversely the probability of an individual plant not growing is q=1-p = 0.1. The probability of exactly k successes in n trials, where the probability of the success of any one trial is p and the probability of failure on any one trial is q=1-p, is given by the Binomial Probability Formula:

     p(k \ successes \ in\  n \ trials) = \dbinom{n}{k} p^k q^{n-k}

    Here p = 0.9, q=0.1, k = 7, and n=9.

    Can you take it from here? What do you get for a final answer?
    Thanks from HallsofIvy
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,696
    Thanks
    1467

    Re: Probability

    The probability that the first doesn't grow is 0.10. The probability that the second doesn't grow is also 0.10. The probability each of the next 0.90. The probability that the first two don't grow and the next 7 do not grow is (0.10)(0.10)(0.90)(0.90)(0.90)(0.90)(0.90)(0.90)(0 .90)= (0.10)^2(0.90)^7. The same kind of argument will show that two not growing and 7 growing in any order is also (0.10)^2(0.90)^7. But then we can show that there are \frac{9!}{7! 2!} such different orders so the probability of "seven grow and two don't" is \frac{9!}{7! 2!}(0.10)^2(0.90)^7.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: May 6th 2013, 10:29 AM
  2. Replies: 0
    Last Post: May 5th 2013, 07:32 PM
  3. Replies: 1
    Last Post: July 11th 2012, 05:42 AM
  4. Replies: 3
    Last Post: May 29th 2010, 07:29 AM
  5. Replies: 1
    Last Post: February 18th 2010, 01:54 AM

Search Tags


/mathhelpforum @mathhelpforum