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23h
comment Volumes of revolution (annular cross sections)
What you asked for has just been done in the answer by reluctant mathematician.
23h
comment Volumes of revolution (annular cross sections)
Use the method of Cylindrical Shells. It can be done by slicing, but is more complicated that way.
1d
comment Rotation of $y=x(1-x)$ about the $x$-axis
You are welcome.
1d
comment Probability dealing with Odds
Let $p$ be the probability. Then $\frac{p}{1-p}=\frac{a}{b}$. Solve for $p$.
1d
comment Rotation of $y=x(1-x)$ about the $x$-axis
This is the first volume calculation you met, $\int_0^1 \pi x^2(1-x)^2\,dx$. Expand and integrate.
1d
revised Dice Roll Probabilities
deleted 24 characters in body
1d
comment Probability of picking all white marbles?
There are $\binom{n}{k}$ equally likely ways to pick $k$ marbles. There are $\binom{5}{5}\binom{n-5}{k-5}$ ways to pick $5$ white and the rest non-white.
1d
comment Probability of picking all white marbles?
I am having a bad day. Will delete, write a correct comment.
1d
comment Probability of Probabilities :)
Yes, $32768$, enough to wallpaper a room. You are sure to win, and also sure to lose money, since the payoff for a winning ticket is undoubtedly much less than $32000$ to $1$.
1d
comment Probability of Probabilities :)
$15$ matches, $2^{15}$ tickets.
1d
reviewed Leave Open Doubt with Absolute Value Inequality
1d
reviewed Leave Open Find the smallest natural number $n$
1d
reviewed Leave Open compositions of n with k even summands and compositions of n-k with k odd summands
1d
comment Distribution of Summation of two discrete random variables
Note that the support set for the sum is $7$ to $19$.
1d
comment Dice Roll Probabilities
The problem was stated clearly, and that is exactly the problem that I solved.
1d
revised Dice Roll Probabilities
added 193 characters in body
1d
answered Dice Roll Probabilities
1d
comment Distribution of Summation of two discrete random variables
I take it that we know nothing about the distributions of $X$ and $Y$ (apart from the supports), and we do not know whether or not they are independent.
1d
comment Is there always a square between two consecutive cubes?
Well, you attempted it, in that you undoubtedly scanned mentally the first few cubes. That is a very important first step, which I should have put down, since I did that reality check before starting to write the proof.
1d
comment Is there always a square between two consecutive cubes?
The answer was clear to you. The rest was grind. Almost anything works, since after a while there are many squares between consecutive cubes. So the required inequalities were not going to give trouble.