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Probability of finding gold in a drill hole?
There are 260 randomly distributed gold grains each of 1 cu.mm size in a 1 cu.m. cube of rock. If I drill a bore hole of 30mm radius through an axis of the block, normal to a face, what is the probalility of getting
1. No gold grain?
2. One gold grain?
3. Two gold grains?
A real life problem!!
2 Answers
- MerlynLv 71 decade agoFavourite answer
Let X = the number of gold grains in the sample.
X follows a binomial distribution, but due to the large sample size and very small probability of success we can use the Poisson approximation to the binomial.
The rate for the Poisson distribution is going to be 260 grains/(1cu.m.)*(30mm)^2*pi*1m = 0.7351
Thus X ~ Poisson(0.7351)
P[X=0]= exp(0.7351)*(0.7351)^0/0! = 0.4794
P[X=1]= exp(0.7351)*(0.7351)^1/1! = 0.3524
P[X=2]= exp(0.7351)*(0.7351)^0/0! = 0.1295
- 1 decade ago
If the gold is uniformly distributed the chance of finding no gold is 99.7%. The bore hole will only see about 0.28% of the total volume. The odds of finding exactly one grain or exactly two grains are much lower than 0.28%.
