Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [probability]

For questions about probability. independence, total probability and conditional probability. For questions about the theoretical footing of probability use [tag:probability-theory]. For questions about specific probability distributions, use [tag:probability-distributions].

The probability that an event occurs is a number in the interval $[0, 1]$, which represents how likely the event is to happen. $0$ indicates it will never happen, $1$ indicates it will always happen.

For example, throwing two dice gives a total of $6$ five times out of thirty-six. We write $$P(X=6)=\frac{5}{36}$$.

Use this tag for basic questions about probability, independence, total probability and conditional probability.

For questions about the theory of probability, use instead. For questions about specific probability distributions, use .

105859 questions
8
votes
2 answers

What is the expected value of the number of circles formed?

There are $99$ identical square tiles, each with a quarter-circle drawn on it. When the tiles are randomly arranged in a $9$ by $11$ rectangle, what is the expected value of the number of full circles formed?
heyhuehei
  • 683
8
votes
10 answers

Should I throw the dice again if I have rolled 4?

My math skills are very basic so it might be a stupid question, I had a discussion with my brother in law and now we have a 'math problem'. We were playing a game with dices and he threw 4. The challenge was to throw the highest number, you can stop…
Sven van den Boogaart
  • 195
8
votes
1 answer

Probability of rounding off a fraction to an even number

In a quiz the following question was asked : ""Let x and y be two random numbers between 0 and 1. What is the probability that $\frac{x}{y}$ rounds to an even number?"" My friend calculated the answer to be $$\frac{5}{4}-\frac{\pi}{4}$$ which is…
Kevin814
  • 81
8
votes
3 answers

Expected number of (0,1) distributed continuous random variables required to sum upto 1

I define $X_i$ as a random variable that is uniformly distributed between (0,1). What is the expected number of such variables I require to make the sum go just higher than 1. Thanks
0fnt
  • 381
8
votes
2 answers

Expected value equals sum of probabilities

Let $X$ be a random variable that takes non-negative integer values. Show that, $$E[X] = \sum^{\infty}_{k=1}P(X \geq k)$$ I'm having trouble following the solution. Could someone help clarify some steps? Thanks. By definition, $$P(X \geq k) =…
Convergii
  • 223
8
votes
3 answers

Deriving joint CDF from joint PDF

The joint probability function of $(X,Y)$ is given by: $$f_{(X,Y)}(x,y) = e^{-x}$$ Which is defined for the values: $$ 0 \le y\le x<\infty$$ $$0\text{ elsewhere}$$ How would I find the cumulative distribution function of $(X,Y)$? I know that the…
YellowPillow
  • 493
8
votes
2 answers

Must every event have a probability?

Is it possible for an event to simply happen for which it is impossible to define any probability? (Note: By "impossible" I don't mean just "impractical" -- I really mean that the event should not follow any probability distribution.) Somewhat…
user541686
  • 13,772
8
votes
4 answers

Elevator Probability Question

There are four people in an elevator, four floors in the building, and each person exits at random. Find the probability that: a) all exit at different floors b) all exit at the same floor c) two get off at one floor and two get off at another…
user148748
  • 159
8
votes
2 answers

An occupancy problem

Consider the scheme of random placing balls into $N=1000$ cells. We continue the procedure of placing balls as long as a last cell remains empty. The process terminates when a ball is placed into this cell. At this moment several cells (or a certain…
Martin Gales
  • 6,878
8
votes
3 answers

Variance of number of runs of consecutive heads in $n$ biased coin flips

Suppose we have a sequence of $n$ coin flips of a biased coin with probability $p$ of being heads. Let $X_n$ be the random variable that records the number of runs of consecutive heads, e.g. THHTHTHH has 3 runs of heads. By linearity of expectation,…
user2566092
  • 26,142
8
votes
1 answer

Consecutive heads in $N$ coin tosses.

Suppose we toss a fair coin $n$ times. We want to show that we can find a run of $\log_2 n - O(\log_2 \log_2 n)$ heads with probability at least $1 - 1/n^c$ for any $c \geq 1$. I realize that there are already questions and answers on stack exchange…
muffle
  • 738
8
votes
2 answers

Calculating expected value and variance of a probability density function

If I was given a probability density function: $$f(y) = \left\{\begin{array}{ll}\frac{3y^2(4-y)}{64} & \textrm{for } 0 \leq y \leq 4\\ 0 & \textrm{elsewhere} \end{array}\right.$$ for expected value would that just be the following…
user125627
  • 369
8
votes
1 answer

In Lotto what is the minimum number of tickets you would need to buy to guarantee at least one 3 number match?

In Lotto (the UK lottery), you pick 6 numbers from a pool of 49. How many tickets would you need to guarantee at least one match of 3 numbers? Wikipedia shows the probability of matching 3 numbers at 55:1. Does that mean if you buy 55 tickets you…
smeghead
  • 83
8
votes
1 answer

Variance of a sum of complex independent random variables

$\newcommand{\Var}{\operatorname{Var}}$Consider the zero mean independent complex random variables $X_1,\dots,X_n$ and the complex constants $a_1,\dots,a_n$. Does the formula for real valued independent random variables carry over to complex case…
triomphe
  • 3,848
8
votes
2 answers

If the coefficients of the quadratic equation $ax^2+bx +c$ are u.i.i.d ran variates in $(0,1)$ what is the probability of roots being real?

If the coefficients a,b,c(taken in order ,c being the constant term) of a quadratic equation are randomly and independenly chosen in the open interval(0,1) what is the probability that both the roots are real?
AgnostMystic
  • 1,654
1 2 3
…
99 100