Question

there are 250 residents in a community. they decided to set up a three person committee to advise them. the members are chosen at random. the first person chosen will become the chair. their racial/ethnic composition is as follows: 50% white. 30% black and 205 latino.
what is the probability of all three members being black? the chair is a white person? the chair is white or Latino?

Answer 1

Question: There are 250 residents in a community. They decided to set up a three person committee to advise them. The members are chosen at random. The first person chosen will become the chair. Their racial/ethnic composition is as follows: 50% white. 30% black and 20% latino.

What is the probability of all three members being black? The chair is a white person? The chair is white or latino?

Solution: Number of white residents: $250*0.5 = 125$, black – $250*0.3 = 75$, latino – $250*0.2 = 50$.

Probability that all three members are black:

$$P\{1-b, 2-b, 3-b\} = \frac{75}{250} \cdot \frac{74}{248} \cdot \frac{73}{248} = \frac{2701}{102920} \approx 0.3^3 = 0.027.$$

Probability that the chair is a white person:

$$P\{1-w\} = \frac{125}{250} = 0.5.$$

Probability that the chair is white or latino:

$$P\{1-w \text{ or } 1-l\} = 1 - P\{\text{not } \{1-w \text{ or } 1-l\}\} = 1 - P\{1-b\} = 1 - \frac{75}{250} = 1 - 0.3 = 0.7.$$

Answer: $P\{1-b, 2-b, 3-b\} = \frac{2701}{102920} \approx 0.027$;

$$\begin{array}{l} P\{1-w\} = 0.5; \\ P\{1-w \text{ or } 1-l\} = 0.7. \end{array}$$