Expert: Paul Klarreich - 9/20/2009

Question
I am having trouble figuring out which "formula" to use to get to 3 of my answers. Our professor gave us the answers to the problems, and we are to show the work of how we got to the answer.

1.  Find the number of permutations: P(7, 4).  (The answer he gave us is 840)  (QUESTION: Is it possible I copied the answer down wrong? Because I tried 2 different formulas from my notes, and there is no way I'm coming up with an answer even remotely close to 840)

2.  There are 17 balls: 10 red and 7 blue. What is the probability of getting a red ball?  (answer he gave us is 10/17).

3. Events A and B are independent. Find the probability of A and B if the probability of A is 1/2 (one-half) and the probability of B is 1/3 (one-third).  (the answer he gave us is 1/15)

Thank you so much for your help ...

Answer
Questioner: Lorri
Country: United States
Category: Advanced Math
Private: No
Subject: Need help figuring out which formulas to use
Question: I am having trouble figuring out which "formula" to use to get to 3 of my

answers. Our professor gave us the answers to the problems, and we are to show the

work of how we got to the answer.

1.  Find the number of permutations: P(7, 4).  (The answer he gave us is 840)  

(QUESTION: Is it possible I copied the answer down wrong? Because I tried 2

different formulas from my notes, and there is no way I'm coming up with an answer

even remotely close to 840)

2.  There are 17 balls: 10 red and 7 blue. What is the probability of getting a red

ball?  (answer he gave us is 10/17).

3. Events A and B are independent. Find the probability of A and B if the

probability of A is 1/2 (one-half) and the probability of B is 1/3 (one-third).  

(the answer he gave us is 1/15)

Thank you so much for your help ...
...............................................

1.  Find the number of permutations: P(7, 4).  

This one you could look up, I think:

P(7,4) means permutations of 7 objects, taken 4 at a time.

Isn't that  7!/3!   from   n!/(n-r)!

Or you just analyze:  

7 ways to pick item 1, then
6 ways to pick item 2, then
5 ways to pick item 3, then
4 ways to pick item 4

Then the counting principle gives you  7 6 5 4, which is the same as"
7 6 5 4 3 2 1
-------------
       3 2 1

and that is 840.

.......................................
2.  There are 17 balls: 10 red and 7 blue. What is the probability of getting a red

ball?  (answer he gave us is 10/17).

You are kidding, right?  

p(event K) = (# elements in K)/(# elements in sample space)
...........................................
3. Events A and B are independent. Find the probability of A and B if the

probability of A is 1/2 (one-half) and the probability of B is 1/3 (one-third).  

(the answer he gave us is 1/15)

You reviewed the definition of independent, didn't you?

A, B are independent if  p(A, given B) = p(A), and p(B, given A) = p(B)

And, since  p(A and B) = p(A, given B) * p(B), you can put those together and say:

If A,B are indep, then P(A and B) = p(A) p(B) = 1/2 * 1/3 = 1/6, exactly what the

teacher said.

Hmmmmmm.  Perhaps a misprint somewhere.