Probability
There are 3 secretaries and 4 reports. What is the probability that each secretary gets atleast one report?
I figured out what the answer is but i want a generalised solution.
I figured out what the answer is but i want a generalised solution.
posted by Swati Gupta at 9:00 PM
8 Comments:
Swati,
referring to your post titled "Hi!", a few posts below this one, and also to the comment made by prateek on it, I would like to say that he is very much incorrect...
f(x)=x+x+x+x+x+x....x times =x*x=x^2.
Therefore, d/dx[f(x)]=2x.
Hence f(x) is very much continous and also very much differentiable!
Prateek is right because if "x" was .75 then you could not have written x^2 as .75+.75+.75...75 times...
that does not make sense..so the thing is that you cannot write y=x^2 as x+x+x+x+x....x times because x is not an integer and not even constant...
To put it more mathematically,
when you write y=x^2 as x+x+x+x...and then differenciate then you r actually calculating
y'=x*d/dx(x)=x*1=x
It’s like taking out one x(times)…
What I mean to say is when you add x –xtimes…you don’t know what x is…
But in the next line, when you say y=x+x+x+x+….x times you are actually taking one x as constant and then adding….
Rather,think of it this way:
Why can't you say,
y = x^2 = x+x+...+x (x times)
= {( 1+1+...+1) (x times)+ (1+1+...+1) (x times) +. . +(1+1+...+1) (x times)}(xtimes)
so y' = 0+0+...+0 (x^2 times) = 0 ?
This time, what we actually calculated was
x^2 * d/dx(1)=x^2*0=0
The correct way to do this is
y = x^2 = xd/dx(x)+xd/dx(x)
y = (1+1+1+ ...x times)*d/dx(x)+(1+1+1... x times)*d/dx(x)
y’= (1+1+1+…x times)+(1+1+1+1+…..x times)
= 2x
(This is from the product rule: if f(x) = u(x)*v(x), then
f'(x) = u'(x)*v(x)+u(x)*v'(x).)
Phew, that was rather a long explanation....
Well I think that should pretty much get the idea into 'Einsteinian Beethoven'. I still hold by my simple explanation that for a function to be differentiable, it has to be continuous and for that it should atleast have a Range of all reals [if we want the function to be differentiable for all values], and since that function is not continuous, it is not differentiable.
Swati this question was taught to me by my maths teacher in the form of letters and their covers. The basic key to solving such questions is to make diffrent cases for different possibilities. Also remember a formula known as beggars to the power biscuits.When you have to distribute some objects to some people the total no. of ways in which you can do so is the no of people (the beggars) to the power the no of objects(biscuits).
so for your problem if we make cases:-
1)each person gets 1 report
2)one person gets 2 reports
(this one will further have three cases)
by getting the no. of ways the event 1,2 can occur you can easily find the probability.
case 1)
as there 4 reports initially
the no. of ways of distributing the reports is 4C1x3C1x2C1
case 2)
as there are three persons we have to select the one who gets two reports this selection can be done in 3C1 ways. then correspondingly multiply it by
4C2x2C1x1C1.
add the value in both the cases and then divide by 3 raised to the power 4 to get the final ans.
Varenya, when you add 4c1*3c1*2c1(=24) and 4c2*2c1*3c1(=36) you get a 60, divided by 3^4 gives you a fraction...which is not possible...
Perhaps, you missed some other operation that had to be done...
a fraction ans is always possible in probability
Probability of any event in the universe we know must lie in the range [0,1], which means that Varenya's answer is very much possible and, as a matter of fact, it is absolutely correct.
Sorry.. I was still thinking in terms of combinations..
Thanks for the ans..
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