The probability that an American CEO can transact business in a foreign language

Question

The probability that an American CEO can transact business in a foreign language is .20. Twelve American CEOs are chosen at random.

a.What is the probability that none can transact business in a foreign language?

b. What is the probability that at least two can transact business in a foreign language?

c. What is the probability that all 12 can transact business in a foreign language?

The probability that an American CEO can transact business in a foreign language is .20. Twelve American CEOs are chosen at random.

a.What is the probability that none can transact business in a foreign language?

b. What is the probability that at least two can transact business in a foreign language?

c. What is the probability that all 12 can transact business in a foreign language?

Explanation / Answer

a) probability that none can transact business in a foreign language = 12C0 (0.20)0(1-0.20)12 =0.0687

b) probability that at least two can transact business in a foreign language = 1 -  probability that at most one can transact business in a foreign language = 1 -12C0 (0.20)0(1-0.20)12 -  12C1(0.20)1(1-0.20)11 = 0.7251

c)  probability that all 12 can transact business in a foreign language = 12C12 (0.20)12(1-0.20)0   = 0.00000000409

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