Advanced Math/Permutations and probabilities
Expert: Paul Klarreich - 9/20/2009
QuestionI 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 ...
AnswerQuestioner: 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.