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=[tex]1-0.20=0.80[/tex]
Total number of American CEOs chosen=12
a. The probability that none can transact business in a foreign language=[tex]12C_0(0.20)^0(0.80)^{12}[/tex]
Using binomial theorem [tex]nC_r(1-p)^{n-r}p^r[/tex]
The probability that none can transact business in a foreign language=[tex]\frac{12!}{0!(12-0)!}(0.8)^{12}=(0.8)^{12}[/tex]
b.The probability that at least two can transact business in a foreign language=[tex]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))[/tex]
c.The probability that all 12 can transact business in a foreign language=[tex]12C_{12}(0.8)^0(0.2)^{12}[/tex]
The probability that all 12 can transact business in a foreign language=[tex]\frac{12!}{12!}(0.2)^{12}=(0.2)^{12}[/tex]
