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.30. Eleven American CEOs are chosen at random. (a) What is the probability that none can transact business in a foreign language? (Round your answer to 4 decimal places.) Probability 0.0198 (b) What is the probability that at least two can transact business in a foreign language? (Round your answer to 4 decimal places.) Probability 0.8870 (c) What is the probability that all 11 can transact business in a foreign language? (Round your answer to 10 decimal places.) Probability

Explanation / Answer

X ~ Binomial(n,p)

n = 11, p = 0.30

P(X) = nCx px (1-p)n-x

a)

P(X= 0) = 11C0 0.30 0.711

= 0.0198

b)

P(X >= 2) = 1 - P( X <= 1)

= 1 - { P ( X = 0) + P( X = 1 ) }

= 1 - { 11C0 0.30 0.711 +11C1 0.31 0.710 }

= 1-0.1130

= 0.8870

c)

P( X = 11) = 11C11 0.311 0.70

= 0.0000017715

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