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?

Answer 1

Answer with Step-by-step explanation:

We are given that

The probability that an American CEO can transact business in  foreign language=0.20

The probability than an American CEO can not transact business in foreign language=$1-0.20=0.80$

Total number of American CEOs  chosen=12

a. The probability that none can transact business in a foreign language=$12C_0(0.20)^0(0.80)^{12}$

Using binomial theorem $nC_r(1-p)^{n-r}p^r$

The probability that none can transact business in a foreign language=$\frac{12!}{0!(12-0)!}(0.8)^{12}=(0.8)^{12}$

b.The probability that at least two can transact business in a foreign language=$1-P(x=0)-p(x=1)=1-((0.8)^{12}+12C_1(0.8)^{11}(0.2))=1-((0.8)^{12}+12(0.8)^{11}}(0.2))$

c.The probability that all 12 can transact business in a foreign language=$12C_{12}(0.8)^0(0.2)^{12}$

The probability that all 12 can transact business in a foreign language=$\frac{12!}{12!}(0.2)^{12}=(0.2)^{12}$