A poll of U.S. teachers found that 67% of teachers are very satisfied with their

Question

A poll of U.S. teachers found that 67% of teachers are very satisfied with their careers. Select three teachers randomly from the population of all teachers.
A. What is the probability that all three teachers will be very satisfied with their careers?
B. What is the probability that none of the three teachers will be very satisfied with their career?
C. What is the probability that at least one of the three teachers will be very satisfied?
Please show work. A poll of U.S. teachers found that 67% of teachers are very satisfied with their careers. Select three teachers randomly from the population of all teachers.
A. What is the probability that all three teachers will be very satisfied with their careers?
B. What is the probability that none of the three teachers will be very satisfied with their career?
C. What is the probability that at least one of the three teachers will be very satisfied?
Please show work.
A. What is the probability that all three teachers will be very satisfied with their careers?
B. What is the probability that none of the three teachers will be very satisfied with their career?
C. What is the probability that at least one of the three teachers will be very satisfied?
Please show work.

Explanation / Answer

Here' are answer to the question below:

These are the params of binomial distrbution:

n= 3

p = .67

a. P(X=3) = 3C3(.67^3)(.33^0) = .301

b. P(X=0) = 3C0(.67^0)(.33^3) = .036

c. P(X>=1) = 1-P(X<1) = 1-P(X=0) = 1-(.036) = .964

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