Question

A council of three people is to be chosen from a group of 4 lawyers, one artist, and 3 teachers

What is the probability to have at least one teacher in the council?
a) .125
b).875
c).3333
d).756​

Answer 1

Answer: 0.2857

Explanation:

At least one teacher means exactly 1 or exactly 2 or exactly 3 teachers. Find the probability of each and add them up.

`\text{One teacher}:(3\ teachers)/(8\ total\ people)*(5\ others)/(7\ people)* (4\ others)/(6\ people)=(5)/(28)=0.1786\\\\\\\text{Two teachers}:(3\ teachers)/(8\ total\ people)*(2\ teachers)/(7\ people)*(5\ others)/(6\ people)=(5)/(56)=0.0893\\\\\\\text{Three teachers}:(3\ teachers)/(8\ total\ people)*(2\ teachers)/(7\ people)*(1\ teacher)/(6\ people)=(1)/(56)=0.0179`

One teacher + Two teachers + Three teachers = 0.2857