An experiment is conducted to select a suitable catalyst for

An experiment is conducted to select a suitable catalyst for the commercial production of ethylene - diamine (EDA), a product used in soaps. Suppose a chemical engineer randomly selects three catalysts for testing among a group of ten catalysts, 6 of which have low acidity and 4 of which have high acidity.

a) Find the probability that no highly acidic catalysts are selected.

b) Find that probability that at least two highly acidic catalyst is selected.

Solution

a)

There are 10C3 ways to choose 3 acids.

There are 6C3 ways to choose 3 non-highly acidic items.

Thus,

P(no highly scidic) = 6C3 / 10C3 = 0.166666667 [answer]

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b)

If two are already highly acidic, then there are 8C1 ways to select the last one.

Thus,

P(at least 2 highly acidic) = 8C1 / 10C3 = 0.066666667 [answer]