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The Peanuts (Posted on 2003-02-18) Difficulty: 3 of 5
Although some of the things in this problem aren't true in real life just assume they are in the question.

When growing peanuts the following happens:

  • for every 2 single chambered peanuts there will be one double chambered peanut
  • for every 2 double chambered peanuts there will be one triple chambered peanut
  • for every 2 triple chambered peanuts there will be one quadruple chambered peanut.

    When a company packages 1000 peanuts in one bag they take peanuts randomly from a giant bin that contins all the peanuts grown. What are the odds that there will be 1000 individual nuts?

  • See The Solution Submitted by Alan    
    Rating: 3.7500 (4 votes)

    Comments: ( Back to comment list | You must be logged in to post comments.)
    Simulation confirmation of probability | Comment 7 of 11 |
    A set of 100,000 trials, using
    RANDOMIZE TIMER
    p1 = 1 / 15: p2 = p1 + 2 / 15: p3 = p2 + 4 / 15
    trials = 100000
    FOR tr = 1 TO trials
    comp = 0
    FOR i = 1 TO 577
    r = RND(1)
    SELECT CASE r
    CASE IS < p1
    comp = comp + 4
    CASE IS < p2
    comp = comp + 3
    CASE IS < p3
    comp = comp + 2
    CASE ELSE
    comp = comp + 1
    END SELECT
    NEXT
    IF comp = 1000 THEN suc = suc + 1
    NEXT
    PRINT : PRINT suc, trials, suc / trials, trials / suc
    resulted in 1814 successes in the 100,000 trials for a probability of .01814 or one in 55.12679, which confirms the 0.01788 posted, as the 1814 successes could have been 43 more or less and stay within one std. deviation. (Poisson dist., std dev = √mean)
      Posted by Charlie on 2003-02-23 11:31:12
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