Question

2. An elementary school employs 20 teachers; 12 are women and 8 are men. Two teachers are selected at random to meet the governor. Is this selection done with or without replacement?

a) What is the chance that both are women?

b) What is the chance that at least one is a women?

c) What is the chance that both are the same gender?

Answer 1

An elementary school employs 20 teachers; 12 are women and 8 are men.

The selection is without replacement since, one teacher can not be chosen twice

a) What is the chance that both are women?

P[ both are women ] =

P[ both are women ] =

P[ both are women ] = 0.3474

b) What is the chance that at least one is a women?

P[ At least one is women ] = 1 - P[ None is women ]

P[ None is women ] =

P[ None is women ] =

P[ None is women ] = 0.1474

P[ At least one is women ] = 1 - 0.1474

P[ At least one is women ] = 0.8526

c) What is the chance that both are the same gender?

P[ Both are same gender ] = P[ Both male ] + P[ Both female ]

P[ Both female ] = 0.3474

P[ Both male ] =

P[ Both male ] =

P[ Both male ] = 0.5053

P[ Both are same gender ] = 0.5053 + 0.3474

P[ Both are same gender ] = 0.8527