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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The Price is Wrong

On a game show, a Showcase Showdown occurs where three contests are asked to spin the Big Wheel which contains 20 sections showing values from 5¢ - $1.00 in increments of 5¢. If in one round of the ...
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0answers
6 views

How to set up this type of probability question

(Problem) A fishing boat has 10 worms and 10 leaches as bait. The bait is chosen at random. Find the probability that the 5th worm is drawn as the 6th draw from the container. Assume that there is ...
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1answer
23 views

Grade 12 Probability

A bag in music class contains 3 tambourines, 4 claves, 6 maracas, and 2 xylophones. If 5 instruments are drawn randomly, determine the number of ways at least 2 tambourines will be drawn.
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1answer
36 views

Hacking with the last four of your SSN

Suppose a hacker gets a hold of the last four numbers of your social security number (the serial number). What is the probability that the hacker randomly guesses your full social security number? ...
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0answers
30 views

Basic Probability Exersices

My answers: a) $3^6$ choices b) The first book has 3 choices, if the second book(3 choices) goes to the first library, the 3rd and 4th fill in the 2nd library the number of choices is $3 \times 3 ...
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0answers
18 views

Probability with a deck of cards [on hold]

Suppose that all five-card poker hands are equally likely (no jokers). What is the probability of being dealt the following hands? (a) 1 pair (a,a,b,c,d are all distinct) (b) Three of a kind ...
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0answers
12 views

Mean squared error of a noisy random variable

Assume we have a distribution D, and a random variable X from this distribution. We want to estimate E(D) through X. Obv E(X) is an estimator for E(D). The question is that does the MSE (=mean squared ...
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1answer
13 views

Mutliplication rule vs. complement principle

If you roll four dice, what is the probability that there will be at least two dice showing the same number? I suppose the answer is 1 - [(6*5*4*3)/6^4] using the complement principle. But would how ...
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0answers
20 views

How to find the probability density function

This may seem trivial but I don't know how to determine the functional form of the probability density function (pdf) for the following case. Will highly appreciate some guidelines on how to go about ...
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0answers
21 views

If a Rubik’s cube is tossed 6 times what is the probability that the cube will land on the red side at least 4 times?

A Rubik’s cube in which each side is painted one of six colors (white, orange, red, blue, green and yellow). Suppose each side of the Rubik’s cube consists of only one color, if the Rubik’s cube is ...
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0answers
27 views

How many Possible Combinations exist?

I have $120$ coins and $21$ buckets. Each bucket can hold $0$ to $20$ coins. How many possible coin/bucket combinations are there?
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1answer
36 views

prove: if B $\subset A$, then Probability(B) $\le$ Probability(A)

B $\subset A$, then P(B) then P(B) $\le$ P(A) I've seen a video to this answer and some yahoo answers to this question but it's still not clear to me how you derive the answer.
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1answer
27 views

Probability of sample mean [on hold]

A town has $500$ real estate agents. The mean value of the properties sold in a year by these agents is $\$800,000$ and the standard deviation is $\$300,000$. A random sample of $100$ agents is ...
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1answer
22 views

Probability mass function - find the second tallest boy in a room.

A kindergarten class consists of $12$ boys and $4$ girls. The children are arranged from tallest to shortest. Assume that all $16!$ rankings are equally likely, and no two children are exactly the ...
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1answer
44 views

Rubiks Cube Landing on Red

A Rubik’s cube in which each side is painted one of six colors (white, orange, red, blue, green and yellow). Suppose each side of the Rubik’s cube consists of only one color, if the Rubik’s cube is ...
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0answers
21 views

Apparantly same probability questions with different answers.

I was reading A first course in probability by Sheldon Ross when and then I came up with this question. This is how he introduces the famous problem of points Independent trails, resulting in a ...
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2answers
19 views

Finding EV and variance of the number of times a word occurs

Consider an iid sequence $X_1, X_2, \dots, X_{n+1}$ taking values 0 or 1 with probability distribution $$P\{X_i=1\} = 1-P\{X_i=0\} = p.$$ Uniformly choose $M$ fragments $F_1, F_2, \dots, F_M$ of ...
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1answer
22 views

An unlikely card game

I was playing this card game and noticed what seems like a very unlikely event. I was wondering how one would compute the probability of it happening. The scenario was that there are ten categories ...
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1answer
12 views

Probability of getting maximum dots in n rolls of a die

A fair die is rolled $n$ times. Let $X_i$ denote the number of spots that are on the up face on roll $i$, for $i=1, 2, \dots, n$. Find the probability mass function of ...
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1answer
38 views

Calculating partitions using multiplication rule

A teacher wants to create 4 study groups of 5 students from a class of 20 students. How many ways are there to do this? The answer is $\binom{20}{5}\binom{15}{5}\binom{10}{5}\binom{5}{5}$. I don't ...
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0answers
26 views

Probability and Expected profit

I really need help for this qn! You are asked to determine the profitability of a new line of sunglasses, which will retail for \$10. The fixed cost of setting up the line is \$2000. The total number ...
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3answers
39 views

When to use $\mathbf{P}$ , and when to use $\mathbb{P}$ as the symbol for probability?

I am trying to make myself some notes in preparatino for my FRM examination. Because I did a little mathematics and mathematical statistics at uni, I am getting very impatient with the inconsistent ...
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2answers
22 views

Flipping several biased coins

Assuming I'm flipping $M$ biased coins with different probability for heads $p_i, i=\{1,...,M\}$. What is the probability of having $k$ times head? Is there a distribution function known for this?
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0answers
9 views

Determine a distribution of a gaussian stochastic at different time

I would like to determine the autocorrelation function of a Gaussian stochastic. Let see my problem So my solution is The distribution of $y=x(t_1)-x(t_2)$ is also a Gaussian stochastic with ...
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0answers
22 views

radius of convergence of series of random variables [on hold]

Let $(X_n)_{n\in\mathbb{N}}$ be a sequence of independent random variables. Let $r$ be the radius o fconvergence of the power series $\sum_{n=1}^\infty e^{X_n}z^n$. Prove that $r$ is a non-random ...
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2answers
53 views

proof of convergence in probability

Let $(X_n)_{n\in\mathbb{N}}$ be i.i.d. random variables taking values in the set of natural number $\mathbb{N}$. Assume that $\mathbb{P}(X_1=i)=p_i>0$ for $i\in\mathbb{N}$. Let $D_n$ denote the ...
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2answers
40 views

How to integrate $ \int\limits_0^\infty{\frac{1}{{\sqrt {({y_1} - {y_2}){y_2}} }}d{y_2}} $?

I tried to do but it does not exist. $$ \int\limits_0^\infty{\frac{1}{{\sqrt {({y_1} - {y_2}){y_2}} }}d{y_2}} $$ Thank you
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2answers
13 views

Alternative hash table analysis

Let us say that we have to hash $n$ elements to $m$ hash slots. Now what could be the average length of a chain. We can assume that prob. that 2 elements will map to a particular location will be ...
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0answers
13 views

Certain parasite Trypanosome

Consider the length of individual trypanosome chosen at random from the population. Find a) $\def\Pr{\operatorname{Pr}}\Pr\{20 < length < 30\}$ I just say 0.41 + 0.21 = 0.62 b) $\Pr\{length ...
2
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0answers
20 views

Permutation & combination for creating housie tickets

A game called housie (similar to Bingo) is played in India. This game is played by a group of people based on a few rules. I need to know how many unique tickets can be printed in one session of a ...
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0answers
9 views

Expected cardinality of intersection of identical sets. [on hold]

Consider, two identical sets S1 and S2, each of size n. Choose 'k' items from set S1 (call it A). Choose 'k' items from set S2 (call it B). What is the expected cardinality of the intersection of A ...
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4answers
44 views

Probability tree question

3 tennis players A,B and C play in a tennis tournament. The first match is between A and B. The winner plays with C and so on until one player wins 2 matches (overall, not necessarily in a row). All 3 ...
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0answers
70 views

How to prove this ?

I hope you are fine . I have a question in Probability theory subject : We know that If X and Y are two random variables , we say that X and Y are equal in distribution (X =d Y) if they have the same ...
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0answers
15 views

How to find an expected value conditional on two random variables? [on hold]

Suppose: $\eta \sim N(0, a^2)$ $\nu \sim N(0, b^2)$ $\eta$ and $\nu$ are independent on each other Let $Y=\theta+\eta\\ X=\theta+\nu$ Then $E(\theta|Y) = Y$ $E(\theta|X) = X$ $E(\theta|X,Y) ...
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1answer
151 views

Probability that the second-best player finishes second in a single-elimination tournament, given that better players always defeat weaker players?

A chess tournament (single-elimination format) has 16 players. Suppose that no two players have the same strength, and that each player always defeats the players weaker than himself/herself (i.e. no ...
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2answers
16 views

Question about probability [on hold]

For a family what is the probability of having five boys in a row? I'm currently taking MATH103, and this question was on our homework. I've tried reading through the book and notes, and not seeing ...
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1answer
17 views

card drawing with replacement

If 6 cards are drawn from a deck of cards with replacement. What is the probability that the outcome is a club at least once. I thought it would be 13/52. But I was wrong.
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2answers
46 views

What is the difference between independent and mutually exclusive event? Explain with example and counter example.

Two events are mutually exclusive if they can't both happen Independent events are events where finding out about one doesn't change the probability of the other. Is it fine ? what should be its ...
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0answers
21 views

Combinations: 6 numbers selected, chance of 3rd largest being 15? [duplicate]

Q: 6 numbers are selected without replacement from the list {2,3,7,8,12,15,17,21,28}. Find the probability that the third largest number is 15. My attempt: There are 9 numbers and 6 can be ...
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0answers
52 views

Prove there exist a $p$ so that the inequality holds

I am stuck with the following problem. Given the Gaussian mixture distribution $f(\cdot)$ $$ f(x) = ...
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2answers
55 views

Finding the probability of choosing six numbers

I just started to learn probability and came across this question: Six numbers are selected without replacement from the list {2, 3, 7, 8, 12, 15, 17, 21, 28}. Find the probability that the third ...
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0answers
20 views

Difference between identity and diagonal covariance matrices

thanks in advance for the help. Suppose I am training a linear model. What are the conceptual differences between using a diagonal covariance matrix and the identity? It is clear to me that the ...
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1answer
32 views

Three dice rolled

Three indistinguishable (fair) dice are thrown simultaneously at random. Find the probability that the sum of the three dice is less than six and that no two dice show the same face (the same number). ...
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3answers
69 views

Moment-generating functions of random variables

Textbook question: Find the MGF of the random variable $X$ with PMF $$p_{X}(x) = pe^{-\lambda}\dfrac{\lambda^{x}}{x!}+(1-p)e^{-\mu}\dfrac{\mu^{x}}{x!}\text{, }\quad x = 0, 1, \dots$$ where ...
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1answer
19 views

Probability that a company is worth $xM after y years, if its value can only stay the same or double every year?

Let's say a company is worth \$1M. Each year, the value of the company eithers stays the same with probability $\frac{1}{2}$, or doubles with probability $\frac{1}{2}$. What is the probability that ...
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1answer
26 views

Probability of getting exactly one correct card when distributing n cards among n people

If I distribute n cards among n people and each person can get one correct card matched his identity. What is the probability that only one person would get the correct card?
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0answers
20 views

Bayes theorem pobability understand [on hold]

A problem A FAMOUS GAME on spoj has a bayes theorem solution. The solution for the same is given in the below image. I am not able to get how to use bayes theorem to come up with the value of S in ...
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0answers
21 views

Independent Brownian motions question

Let $B$ and $W$ be independent Brownian Motions and let $\tau$ be a stopping time of $W$. Is it true that $E[\int_0^{\tau} B_s \, dW_s] = 0\text{ ?}$ So far I have tried the following: The integral ...
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4answers
64 views

Probability of at least 3 red balls given 4 choices in a bag of 4 red balls and 4 black balls?

Let's say there are 8 balls in a bag, where 4 are red and 4 are black. If I choose four balls from the bag without replacement, what is the probability that I will choose at least 3 red balls? My ...
0
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2answers
26 views

Let $f(x) = ax^{-a-1}$ for $x \geq 1$ and $f(x) = 0$ otherwise …

Let $f(x) = ax^{-a-1}$ for $x \geq 1$ and $f(x) = 0$ otherwise, where '$a$' is a positive parameter. Show how to generate random variables from this density from a uniform random number generator. ...