AboutPaul Klarreich Expertise I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction.
I can also try (but not guarantee) to answer questions on Abstract Algebra
-- groups, rings, etc. and Analysis -- sequences, limits, continuity.
I won't understand specialized engineering or business jargon.
Experience I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.
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
