Question

Without using Excel (in other words - long hand) A box contains 100 thermometers, of which 10 are defective. You reach in and randomly take 5 thermometers from the box all at once. Let X be the number of non-defective thermometers in your selection. (a) What is the probability that all of the five thermometers are non-defective (that is, that X = 5)? (b) What is the probability that at least 2 of the five thermometers are non-defective? (c) What is the name of the probability distribution for X?

Answer 1

n =    5
non defective, k =   90
total , N =   100

it is hypergeometric distribution
and probability is given by
P(X=x) =C(k,x)*C(N-k,n-x)/C(N,n)

A) P(X=5)= C(90,5)*C (10,0)/C(100,5)           =   0.5838

B)  P(X=0)= C(90,0)*C (10,5)/C(100,5) = 0.0000

P(X=1)= C(90,1)*C (10,4)/C(100,5) = 0.0003

P(X≥2) = 1- P(X=0) - P(x=1)  =1 - 0.000 - 0.0003 = 0.9997

C) Hypergeometric Distribution

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