Thread: Two study questions

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

Originally Posted by Danneedshelp

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.

What is the probability of selecting three black balls? Three red balls? Three white balls?

CB

Originally Posted by Danneedshelp

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.

There are now two types of ball 8 (black or white) balls and 4 red balls.

So the expected number of (black or white) balls is:



where is the probability of exactly (black or white) balls in three draws without replacement.

CB

Originally Posted by CaptainBlack

What is the probability of selecting three black balls? Three red balls? Three white balls?

CB

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?

Originally Posted by CaptainBlack

There are now two types of ball 8 (black or white) balls and 4 red balls.

So the expected number of (black or white) balls is:



where is the probability of exactly (black or white) balls in three draws without replacement.

CB

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

Originally Posted by Danneedshelp

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?

You should not need to use the hypergeometric distribution explicitly, you should just be able to write these down.

Your P(B)=(3/12)(2/11)(1/10) etc.

CB

Originally Posted by Danneedshelp

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

No that is not what I wrote, and I did mean exactly what I did write.

CB