Results 1 to 2 of 2

Math Help - Binomial distribution.

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    3

    [SOLVED] Binomial distribution.

    Solve this problem:
    Six calculators are bought. The probability of a calculator breaking down within two years is 0.25. Calculate the probability that within two years:

    a) Exactly two of six calculators break
    b) Three at most break
    c) At least 3 break
    d) Either two or three break
    Last edited by Kane535; May 16th 2010 at 11:59 AM. Reason: Re-titled.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by Kane535 View Post
    Solve this problem:
    Six calculators are bought. The probability of a calculator breaking down within two years is 0.25. Calculate the probability that within two years:

    a) Exactly two of six calculators break
    b) Three at most break
    c) At least 3 break
    d) Either two or three break
    Hi Kane535,

    this is a binomial situation in which a calculator breaks down within 2 years or doesn't.

    (p+q)^6=\binom{6}{0}p^6q^0+\binom{6}{1}p^5q^1+\bin  om{6}{2}p^4q^2+\binom{6}{3}p^3q^3+\binom{6}{4}p^2q  ^4+\binom{6}{5}pq^5+\binom{6}{6}p^0q^6

    where p=probability of a breakdown in 2 years, which is 0.25

    q=probability the calculator is still functional after 2 years, which is 1-0.25=0.75.

    \binom{6}{n}p^{6-n}q^n is the probability of having exactly n functional calculators after 2 years.

    (a)

    \binom{6}{4}p^2q^4=\binom{6}{2}p^2q^4

    (b)

    At most 3 is 3 or less, which is 0, 1, 2 or 3 breakdowns

    \binom{6}{3}p^3q^3+\binom{6}{4}p^2q^4+\binom{6}{5}  pq^5+\binom{6}{6}q^6

    (c)

    At least 3 is 3, 4, 5 or 6 breakdowns

    \binom{6}{0}p^6+\binom{6}{1}p^5q+\binom{6}{2}p^4q^  2+\binom{6}{3}p^3q^3

    (d)

    Either 2 or 3

    \binom{6}{3}p^3q^3+\binom{6}{4}p^2q^4
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Binomial Distribution
    Posted in the Statistics Forum
    Replies: 6
    Last Post: November 18th 2011, 12:48 PM
  2. Replies: 3
    Last Post: March 21st 2010, 05:25 PM
  3. Replies: 1
    Last Post: November 12th 2009, 12:38 AM
  4. Replies: 1
    Last Post: March 11th 2009, 11:09 PM
  5. Cumulative distribution function of binomial distribution
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: October 31st 2008, 03:34 PM

Search Tags


/mathhelpforum @mathhelpforum