Question

In a community there are two families black and white. 10 families are selected to be interviewed about the school district.what is the probability of all families are white and probability of all 10 families are black? if all ten are selected as either all white or all black would you consider this a racial bias in the selection?

Answer 1

There are two families. So, while selecting a family to be interviewed, there is a probability $\mathrm{P}_1 = \frac{1}{2}$ to select a black family and a probability $\mathrm{P}_2 = 1 - \frac{1}{2} = \frac{1}{2}$ to select a white one.

Using the multiplying rule, if families are selected randomly, the probability of all 10 families being black is $(1/2)^{10} = 1/1024$.

The probability is very small, so, if all selected people are either white or black, we would consider this as a racial bias in the selection.