The probability that an American CEO can transact business i

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?

Solution

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