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?

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