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...
and
Given by Tchebysheff's Theorem . So, k=4 and thus
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
So, If I let B represent the event of choosing three black balls, R the event of choosing three red balls, and W represent the event of choosing 3 white balls I need to find
by using the hypergeometric dist for each probability. So, I only need to change my r value each time. Correct?
The refers the collection of objects with the desired properties, so in this case, (black or white). Hence, each probability you showed above is hypergeomentric with , and ?
Thanks a lot for your help, I really appreciate it.
Can someone check my work for the Tchebysheffs propblem