On this website (http://www.sciencenews.org/view/generic/id/60598/title/When_intuition_and_math_probably_look_wrong), I recently came across a twist on the Two Children Problem. The problem is deceptively simple: "I have two children, one of whom is a boy born on Tuesday. What is the probability...
In poor countries, the domestic electricity supply is inconsistent, and even though the country's standard voltage may be 220V, it is not unusual for the voltage to go quite a bit below this level, say around 150V.
So normally, households buy step-up transformers, so that they can increase...
I don't understand it completely myself, but let me try to provide a shorter version of this answer.
Question: I have two dice. If i roll them until i get a double, which is the most likely roll to get a double on?
It is explained in the answer that, since he will stop rolling when he...
There's a probability question I saw on the web that looks innocent enough, unless you pay attention to the wording:
I have two dice.
If i roll them until i get a double, which is the most likely roll to get a double on?
The answer given is below:
The first roll is the most likely.
Heres...
I found the following posted in another forum:
He did not cite the source.
He suggests that this is related to Relativity. I'm no relativity expert but I doubt the authenticity of his claims, especially the part that the rotation of a planet affects its gravitational pull. What do you think?
Yeah, I messed that up and got a weird number because I kept thinking that any gas that expands must cool. Mathematically,
Energy of the gas at equilibrium = \Delta_U = mc\Delta_T
Since there is no change in energy, \Delta_U=0 and therefore
mc\Delta_T = 0
Since the mass m and...
I've been working on the following problem for several hours but am not sure how to approach part (c).
Consider the insulated vessel shown here, with compartment A of volume 0.03 m3, which is empty, and separated by an insulating membrane from compartment B of volume 0.01 m3, which contains...
Quite briefly, sets are a way of representating things in logic and other areas of mathematics. It's not really a matter of difference and likeness.
Unfortunately we do not help with finding websites. That's what Google is for. :)
Another one I absolutely could not do (and this time I'm sure it's not due to fumbling algebra) is this:
Prove by induction that (1 + 1/4 + 1/9 + ... + 1/n^2) is less than (2 - 1/n) for all integers greater than 1.
I get the base step, then make the assumption p(k) is true. Then I add...
Arrrrgh damn it, no wonder I couldn't get it right. I got the binomial expansion wrong! Thanks a lot, Tide, and that's a neat second proof. Can't believe I wasted a couple hours due to a stupid slip-up...
I've been working on this problem for the past two and a half hours. The problem is: Prove by induction that n^3 + 2n is divisible by 3 for non-negative integer values of n.
No matter how I try, I cannot manipulate the expression of the inductive step so that it is divisible by 3.
I have...
Current across a node?
In the attached circuit diagram, I have found the values of everything except I5 (shown with the red arrow).
Applying Kirchoff's Current Law to the intersection of R1 and R3 came to mind, but then I saw that I5 itself is on a node! If I applied KCL at this node, the...