This tag is for basic questions about probability and for questions in which one wants to calculate a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using measure theory), please ask under ...

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1answer
150 views

How to solve probability questions?

Jack and Jill were both sent to the blue room for not completing their probability assignment on time. When they reported to the blue room, they were each given an envelope with either a green or red ...
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4answers
4k views

How many 32 digit binary number combinations are possible?

How many 32 digit binary number combinations are possible? For example: $$00000000-00000000-00000000-00000000$$ $$00000000-00000000-00000000-00000001$$ $$00000000-00000000-00000000-00000010$$ $$.$$ ...
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0answers
73 views

impossibility of Axiom 3 of probability

Suppose $S = [0,1]$ and $P$ is a uniform probability measure. Find a countable collection of subset of $S$, $A_1, A_2, A_3,\dots$ such that they are pairwise disjoint but $P(\cup A_i) \neq \sum ...
2
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2answers
501 views

The largest of $N$ random numbers over a uniform distribution?

So I read somewhere than if you have $N$ numbers picked independently from a uniform distribution, say $[0,1]$, the greatest number has an expected value of $\frac{N}{N+1}$. So if you have 2 numbers ...
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1answer
6k views

Two cards are drawn without replacement from an ordinary deck, find the probability..

Two cards are drawn without replacement from an ordinary deck, find the probability that the second is a red card, given the first is a red card. P (2nd Red Card / 1st Red Card) = 13/52 * 12 * 51 = ...
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3answers
488 views

if one three digit number (0 cannot be left digit) is chosen at random from all those that can be made from this set that are not a multiple of 5.

Set = {0,1,2,3,4,5,6} The left digit would have 6 possibilities since 0 cannot be the left digit. The middle one would have 7 possibilities. The right digit would have 2 possibilities 0 and 5? Am I ...
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2answers
2k views

What is the probability of getting a sum of 7 or at least one 5 when you roll two die

Please tell me how to approach this problem. (Sum of 7) = {4+3, 3+4, 6+1, 1+6, 5+2, 2+5} = 6 (At Least one 5) = {1+5, 2+5, 3+5, 4+5, 6+5, 5+1, 5+3, 5+4, 5+5, 5+6} = 10 so the answer will be 16/36 ...
3
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1answer
105 views

Probability to draw a white ball from the third box.

There are $2$ boxes full of black and white balls. The first one has $a$ white and $b$ black balls ($a\geq2$ && $b\geq2$). The second one has $c$ white and $d$ black balls ($c\geq1$ && ...
4
votes
2answers
95 views

$P(X \ge 450)$ in Possion distribution

The number of pedestrians that cross the street in one minute has Poisson distribution $\def\Pois{\operatorname{Pois}}\Pois(8)$. Find the probability that at least $450$ pedestrians will cross the ...
1
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2answers
35 views

Help in solving Conditional Probability problem

I appreciate the help I have received in the past. Please help solve this problem. It holds the key to my understanding of other similar questions. "A box contains 7 marbles, numbered from 1 to 7 ...
2
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1answer
68 views

A philosophical question on randomness

I have read in some book the following "philosophical" statement : "Introducing randomness we can make unstable things stable". Is there any practical example of this statement.
0
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1answer
55 views

Does knowledge affects probability?

A bag contains 5 coins: 2 are double-headed, 1 is double-tailed and 2 are normal. (a) You close your eyes, pick a coin at random and toss it. What is the probability that the lower face is heads? (b) ...
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2answers
36 views

Looking for a function that gives more weight to more “data points”, i.e. 30/60 > 1/2

I'm looking to calculate "conversion rates" of some items, as follows: (number of times the item was clicked on) / (number of times the item was presented to the user) I want to give a higher ...
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0answers
1k views

Weighted Probability Problem

Lets say, few independent events are happening. $E_1, E_2,...,E_n$. The probability of each of these events happening is given as $P_1,P_2,...,P_n$. Each of these events carry weightage, say ...
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0answers
34 views

probabilistic location of points with normally distributed distances

I have a set of points (position-sensors) in 3D space attached to a structure which may be more or less rigid. At a given time each point may be in observed or unobserved state. My question is how to ...
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2answers
47 views

Expectation of a distribution

Let $X$ follows binomial(100,0.25). How can I calculate $E(2^X)$? That is I want to find the expected value of $2^X$.
2
votes
1answer
176 views

How come $P(Z< -1.5)$ is equal to $P(Z > 1.5)$ which are both equal to $1-P(Z < 1.5)$?

I can't wrap my head around the idea they are both equal. I mean shouldn't we have $P(-Z > 1.5)$ which is not equal to $P(Z < 1.5)$?
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2answers
89 views

How Many Combinations of $3$ zeros and $2$ ones

I'm rusty on combinations and permutations. I'm dealing with groups of binary numbers. Each group is five digits long, and they all have $2$ "$1$'s" and $3$ "$0$'s". Ex: "$10100$". I'm trying to ...
2
votes
0answers
130 views

Probability of getting at least one ball of each color

Given that we have an urn containing $N=\sum{N_i}$ balls, $N_1$ of color $1$, $N_2$ of color $2, \dots, N_k$ of color $k$, we draw $m$ balls from the urn such that $m \geq k$ and $m \leq \max(N - ...
1
vote
1answer
167 views

Length of longest path in Erdos Renyi graph

Is it possible to compute the expected length of the longest simple path in an Erdos-Renyi graph or even the probability density function of this length?
1
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1answer
93 views

Distribution of gaps between points

If you choose $n-1$ points uniformly and independently at random from the unit interval, what is the distribution of the lengths of the $n$ intervals without points in them? To make it a little more ...
4
votes
2answers
228 views

Probability in a deck of cards to have two jacks in a row

In a deck of $36$ cards ($9$ cards per color, $4$ colors) what is the probability to have $2$ jacks (or more) that follow each other?
2
votes
1answer
94 views

Coin with claim#1: fair, claim#2: P(head)=0.6, refute at least one with 99% chance

I've encountered the following problem, and would like to receive some help: We have a coin. $A$ claims it's a $fair$ one, $B$ claims it has a $60\%$ probability of getting a $head$. What is the ...
0
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1answer
135 views

First Order Stochastic Dominance

I am reading up on stochastic dominance(http://en.wikipedia.org/wiki/Stochastic_dominance) and have some questions: PDF and CDF of Gamble A and B look like this. Since the CDF of A is always less ...
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0answers
72 views

1000 nuts in 500 cakes, random variable X = the number of nuts in a random cake

A baker puts $1000$ nuts the mixture for making $500$ cakes. $X$ is a random variable indicating the number of nuts in a randomly chosen cake, which is at most 5. Find the distribution of $X$ and the ...
0
votes
1answer
53 views

Probability Density Function to Cumulative Density Function

I am reading on Stochastic Dominance (http://en.wikipedia.org/wiki/Stochastic_dominance) and few questions on PDF and CDF. The paragraph I am looking at this: Why is that $P[A\ge x] \ge P[B \ge x] ...
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2answers
129 views

probability of fourth ball is black

suppose that bag contains $3$ red and $5$ black ball,each ball one by one,without replacement is selected at random,what is a probability that fourth ball is black?probability from the beginning of ...
0
votes
2answers
61 views

Integration of Probability density function

I have a question on how this equation changes from Probability Density Function to Cumulative Density Function. The equation $\int U(W)[f(W)-g(W)]\mathrm dW > 0$ changes into $\int U(W) ...
2
votes
2answers
182 views

How many times must you roll a die until each side has appeared? [duplicate]

Let $X$ be the random variable which denotes the number of times a die has been rolled till each side has appeared. The order does not matter. We are trying to find $E[X]$. Let $X_i$ be a random ...
0
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1answer
82 views

Statistics: convergence in probability

Suppose that you are trying to collect a complete set of $n$ baseball cards. Suppose you buy them one at a time and each time you get a randomly chosen card. Let $N_n$ be the number of cards you have ...
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1answer
174 views

N white and black balls and N boxes Probability

Given $N$ boxes , $N$ white balls and $N$ black balls chooses one box randomly and one ball from it randomly Find the probability of getting white ball.
3
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2answers
266 views

Expected number of trials until n-th success urn problem without replacement

I have a close relative of the urn problem, but with a slight twist. Given an urn containing $r$ red balls and $b$ blue balls, how many balls should I expect to pull out of the urn before I have ...
1
vote
1answer
119 views

Gradient ascent, log likelihood

Good day, hi, would like to ask a question. If you have some spare time please kindly enlighten me on the following question. Gradient ascent: $=\sigma \leftarrow \sigma + \dfrac{d}{d\sigma} p(y\mid ...
1
vote
1answer
76 views

combining conditional probabilities

I've come across a physics paper in which pdf $$ p(a|b) $$ is desired, but only $$ p(a|c)\\ p(c|b) $$ are known. It is claimed that $$ p(a|b)=\int p(a|c)p(c|b) dc. $$ Is this correct wlog? I can't ...
2
votes
1answer
66 views

Probability that I win more than three dollars.

There are three slot machines. The prize money in each is 1,2,3 dollars respectively; The probability of winning in respective slot machines is 0.1, 0.4, 0.7 respectively. What is the probability ...
6
votes
1answer
187 views

Probability that a random edge coloring of the complete graph is proper

Suppose we color the edges $\{1,\ldots, {n \choose 2}\}$ of the complete graph on $n$ vertices with $m$ colors each edge being assigned a color picked uniformly at random from $\{1,\ldots, m\}.$ I ...
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1answer
46 views

Finding Variance of max choosing two prime numbers

a) two numbers are chosen from n first prime numbers (repetitions are allowed). If the first is X and the second is Y, find the distribution and variance of $M=max(X,Y)$ b)assume now we ...
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2answers
2k views

How to prove: Moment Generating Function Uniqueness Theorem

Many results are based on the fact of the Moment Generating Function (MGF) Uniqueness Theorem, that says: If $X$ and $Y$ are two random variables and equality holds for their MGF's: $m_X(t) = ...
0
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2answers
28 views

represent probability as fraction

let us consider following problem: we have $20$ light bulb,of which $2$ is defective,we take two bulb randomly and simultaneously ,what is probability that neither of them will be defective? i am ...
0
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3answers
209 views

N Students Probability

*Let there be n students each having x[i] balls in their hands. There are two boxes in front of them one by one they come and keep their balls in any one of the boxes ,each student having probability ...
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2answers
247 views

Expected value of ejecting balls from a jar

in a jar there are $n_1$ black balls,$n_2$ white balls and $n_3$ red. ($n_1,n_2,n_3\ge2$). The balls are ejected one by another and after they are returned to the jar. What is the expected value of ...
1
vote
1answer
76 views

Poisson Mean Problem

The number of home runs in a baseball game is assumed to have a Poisson distribution with a mean of 3. As a promotion, a company pledges to donate $10,000 to charity for each home run hit up to a ...
0
votes
1answer
58 views

Finding covariance for choosing two of n prime numbers

Assume we choose two different numbers of the first n primes (Where X is the first number and Y is the second number was chosen), find the common probability distribution, covariance and $\rho ...
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2answers
344 views

Bayes' Theorem - any trick to figuring out what your E and F are?

I'm having a lot of trouble figuring out what my E and F are supposed to be in Bayes' Theorem problems. Are there any tricks to this? Here's a really hard one for example... A space ship communicates ...
2
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1answer
191 views

Variable substitution in probability

In modeling the number of claims filed by an individual under an automobile policy during a three-year period, an actuary makes the simplifying assumption that for all integers $n \ge 0$, ...
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1answer
97 views

Conditional Expectation Involving Sum of Correlated RVs

Is it possible to find the $E[X_i | \sum_j X_j \geq c]$ where $c$ is a known constant and the $X_j$ are correlated random variables. $X_i$ is in the $X_j$ terms. I know the correlation matrix between ...
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vote
2answers
904 views

Derivative of Standard Normal Inverse

How can I calculate the derivative of the standard normal inverse. I think the derivative of $\Phi^{-1}(x)$ is $$\frac{1}{\phi(\Phi^{-1}(x))}.$$ I would like to know how to find the derivative of ...
6
votes
1answer
82 views

Bridge HCP held by the best hand at the table?

In the game of Bridge, what is the expected number of high card points held by the player holding the most high card points at the table? $A=4$, $K=3$, $Q=2$, $J=1$.
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0answers
65 views

A nice probabilistic problem

In an exam each student must answer $n$ yes-no questions. We know that no two students have answered all $n$ questions the same. We correspond to each question randomly and uniformly an score between ...
0
votes
1answer
49 views

Histogram Intervals

I would like to know if there is any reason to choose some unusual numbers as the histogram edges? Let me explain this better. At one point in my statistics book ( Principle of statistics by Bulmer) ...