Question

Selecting Condiments A box of condiments has ten small packages, in which three are ketchup, three are mustard, and four are relish. A sample of three packages is randomly selected (without replacement) from the box.

What is the probability that at most one mustard package is selected?

What is the probability that at least one mustard package is selected?

What is the probability that X is within one standard deviation from its mean?

Please explain steps

Answer 1

A box of condiments has ten small packages, in which three are ketchup, three are mustard, and four are relish.

P(at most one mustard ) = P(0 musturd) + P(1 musturd) = 7C3/10C3 + 3C1*7C2/10C3 = 0.8167

P(at least one musturd) = 1 - P(no musturd) = 1- 7C3/10C3 =  0.7083

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3)

Sample size,     n =    3
No. of events of interest in population    , k =   3
Population size   , N =   10

mean = E(X) = n(k/N) = 3*3/10 = 0.9
variance = VAR(X) = nk/N*(1 - k/N)((N-n)/(N-1))    0.4900

std dev = √variance =    0.7000

P(µ-σ<x<µ+σ) = P(0.9-0.7<X<0.9+0.7) = P(0.2<X<1.6) = P(X=1)= C(3,1)*C (7,2)/C(10,3)           =   0.5250
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