Question

The probability that an American CEO can transact business in a foreign language is .20. Ten 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 (b) What is the probability that at least two can transact business in a foreign language? (Round your answer to 4 decimal places.) Probability (c) What is the probability that all 10 can transact business in a foreign language? (Round your answer to 5 decimal places.) Probability

Answer 1

Answer:

(a) 0.1074

(b) 0.6342

(c) 1.024 x 10⁻⁷

Step-by-step explanation:

This problem can be modeled as a binomial probability with probability of success (transacting business in a foreign language) p =0.20, and n = 10 trials. The binomial probability model is:

$P(X=x) = \frac{n!}{(n-x)!x!}*p^x*(1-p)^{n-x}$

(a) None can transact business in a foreign language, P(X=0)

$P(X=0) = \frac{10!}{(10-0)!0!}*0.2^0*(1-0.2)^{10-0}\\P(X=0) = 0.8^{10} = 0.1074$

(b) At least two can transact business in a foreign language

$P(X\geq2) = 1-(P(X=0)+P(X=1))\\P(X\geq2) = 1-(0.1074+\frac{10!}{(10-1)!1!}*0.2^1*(1-0.2)^{10-1})\\P(X\geq2) = 1- (0.1074+10*0.2*0.8^{9}) = 0.6342$

(c) All 10 can transact business in a foreign language

$P(X=10) = \frac{10!}{(10-10)!10!}*0.2^{10}*(1-0.2)^{10-10}\\P(X=10) = 0.2^{10} = 1.024 * 10^{-7}$