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

Step-by-step explanation:

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

$\text{One teacher}:\dfrac{3\ teachers}{8\ total\ people}\times\dfrac{5\ others}{7\ people}\times \dfrac{4\ others}{6\ people}=\dfrac{5}{28}=0.1786\\\\\\\text{Two teachers}:\dfrac{3\ teachers}{8\ total\ people}\times\dfrac{2\ teachers}{7\ people}\times\dfrac{5\ others}{6\ people}=\dfrac{5}{56}=0.0893\\\\\\\text{Three teachers}:\dfrac{3\ teachers}{8\ total\ people}\times\dfrac{2\ teachers}{7\ people}\times\dfrac{1\ teacher}{6\ people}=\dfrac{1}{56}=0.0179$

One teacher + Two teachers + Three teachers = 0.2857