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=
`(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=
`(12!)/(12!)(0.2)^(12)=(0.2)^(12)`