11 out of 36? I got this by writing down the number of possible outcomes (36) and then counting how many of the pairs had a 6 in them (1,6) (2,6) (3,6) (4,6) (5,6) (6,6) (6,5) (6,4) (6,3) (6,2) (6,1). Is this correct?

I was trying to answer this question. Find the probability of getting a full house from a $52$ card deck. That is, find the probability of picking a pair of cards with the same rank (face value), and a triple with equal rank (different from the rank of the pair of course). My idea was […]

Suppose that we have two different discreet signal vectors of $N^\text{th}$ dimension, namely $\mathbf{x}[i]$ and $\mathbf{y}[i]$, each one having a total of $M$ set of samples/vectors. $\mathbf{x}[m] = [x_{m,1} \,\,\,\,\, x_{m,2} \,\,\,\,\, x_{m,3} \,\,\,\,\, … \,\,\,\,\, x_{m,N}]^\text{T}; \,\,\,\,\,\,\, 1 \leq m \leq M$ $\mathbf{y}[m] = [y_{m,1} \,\,\,\,\, y_{m,2} \,\,\,\,\, y_{m,3} \,\,\,\,\, … \,\,\,\,\, y_{m,N}]^\text{T}; \,\,\,\,\,\,\,\,\, […]

I heard an interesting question recently: What is the minimum number of people required to make it more likely than not that all 365 possible birthdays are covered? Monte Carlo simulation suggests 2287 ($\pm 1$, I think). More generally, with $p$ people, what is the probability that for each of the 365 days of the […]

I’ve seen many variations of this problem but I can’t find a good, thorough explanation on how to solve it. I’m not just looking for a solution, but a step-by-step explanation on how to derive the solution. So the problem at hand is: You have m balls and n bins. Consider throwing each ball into […]

A two-sided coin has just been minted with two different sides (heads and tails). It has never been flipped before. Basic understanding of probability suggests that the probability of flipping heads is .5 and tails is .5. Unexpectedly, you flip the coin a very large number of times and it always lands on heads. Is […]

There is a cube and an ant is performing a random walk on the edges where it can select any of the 3 adjoining vertices with equal probability. What is the expected number of steps it needs till it reaches the diagonally opposite vertex?

Let $Y_1, Y_2, …$ be independent and identically distributed random variables in $(\Omega, \mathscr{F}, \mathbb{P})$ s.t. their distributions are continuous and $$F_{Y}(y) := F_{Y_1}(y) = F_{Y_2}(y) = …$$ For $m = 1, 2, …$ and $i \le m$, define $$A_{i,m} := (\max\{Y_1, Y_2, …, Y_m\} = Y_i), B_m := A_{m,m}$$ Is it really that $$P(B_m) […]

I know there’s no uniform distribution for a countably infinite set, but I’m wondering if there’s still a way to determine the probability of picking from a subset of a countably infinite set. For example, what’s the probability that I pick an odd number from the set of naturals, assuming I’m picking randomly? Is this […]

What’s the probability that a n-sided polygon made from n distinct random points on circle contain the centre?

Intereting Posts

Perron-Frobenius theorem
Logic and number theory books
What can be said if $A^2+B^2+2AB=0$ for some real $2\times2$ matrices $A$ and $B$?
Show that $g(x,y)=\frac{x^2+y^2}{x+y}$ with $g(x,y)=0$ if $x+y=0$ is continuous at $(0,0)$.
What is the coefficient of $x^{2k}$ in the $n$-th iterate, $f^{(n)}(x)$, if $f(x)=1+x^2$?
The kernel of the transpose of the differentiation operator – Solution check
Let $n \geq 1$ be an odd integer. Show that $D_{2n}\cong \mathbb{Z}_2 \times D_n$.
When does $V=L$ becomes inconsistent?
$-1$ as the only negative prime.
Memoryless property of the exponential distribution
Fourier transform of the Heaviside function
Quasicomponents and components in compact Hausdorff space
What do $\pi$ and $e$ stand for in the normal distribution formula?
How many connected components does $\mathrm{GL}_n(\mathbb R)$ have?
On a $p$-adic unit and the existence of its $n$-th root