Q1: An urn contains 3 black, 4 red, and 5 white balls. Three balls are randomly drawn one at a time without replacement.

a. Find the probability all three balls are of the same color.

b. How many balls would you expect to be black or white?

A1: a) Let N=12, n=3, r=3(same color balls)

So, I used the above info to compute P(Y=3) using the hypergeometric dist and got 0.004545.

b) I am a little thrown off by the "or" in the question. Some help would be great.

Q2: Suppose Y , the number of fatal car accidents in a certain state, obeys a Poisson distribution with an average of four fatal accidents per day.

a. For a particular day, what is the probability that there is at least one fatal car accident?

b. Using Tchebysheff ’s thoerem, find an upper bound for P (Y

≥ 12).

A2: a) simple

b) I am stuck on this part. Here is some of work...

$\displaystyle \mu=\lambda=4$ and $\displaystyle \sigma=2$

Given $\displaystyle P(Y\geq\\12)\rightarrow$ by Tchebysheff's Theorem $\displaystyle P(|Y-4|)\geq\\k2)\leq\\\frac{1}{k^{2}}$. So, k=4 and thus $\displaystyle P(|Y-4|)\geq\\8)\leq\\\frac{1}{16}$

That is what I have done so far, but I am not sure I am on the right track.

Any help would be great. I am trying to straighten some things out before my exam on Thursday.

Thanks