0
votes
1answer
18 views

Probablity nCr problem days of week 3 chosen.

Straight from my daughter's math book :) You work 3 evenings. Your boss assigns you 3 evenings at random from 7. What's the probability of Friday being chosen. We did this long hand (drew out all ...
0
votes
2answers
18 views

Probability of weather on consecutive days.

Probability of a cloudy day is .55 Probability of a sunny day is .45 A)What is the probability of three consecutive cloudy days, followed by a sunny day? B)What is the probability that exactly 1 out ...
1
vote
2answers
43 views

Probability, chose two skittles, out of 2 skittles left from a bag of skittles with 5 colors.

so me and my friend are studying statistics but we are just stuck on this stupid skittle question we made up ourselves when we tried to guess the colors of the two last skittles so we can see who will ...
-1
votes
0answers
11 views

Using BCR experiment [on hold]

consider a random experiment of observing a mechanical or electrical unit consisting of five components and determining which components are working and which have failed. Use the BCR to find the ...
0
votes
2answers
19 views

probability, need help to differentiate distinct or non-distinct

I am having trouble to understand the problems based on combinatorics. In particular, I don't understand when to think in terms of disctinct object or non-disctinct object. Here is one question: ...
1
vote
1answer
33 views

Probability of number formed from dice rolls being multiple of 8

A fair 6-sided die is tossed 8 times. The sequence of 8 results is recorded to form an 8-digit number. For example if the tosses give {3, 5, 4, 2, 1, 1, 6, 5}, the resultant number is $35421165$. ...
2
votes
1answer
32 views

Probability of drawing 4 green balls from an urn when you're the last person to draw

An urn contains 24 balls, 8 of them being white, 8 green and 8 black. There are 6 people sequentially drawing these balls out of the urn (without replacement), with every person drawing 4 balls, and ...
4
votes
2answers
91 views

Fraction Problem. 3rd grader question got parents thinking

So our nine year old son comes home from 3rd grade and tells us an amazing thing happened in school today. He was playing a math game with his friend and they got the same score two times in a row! ...
2
votes
2answers
16 views

Probability Question - team draw from field of 32

For a sport tournament where two-man teams are drawn from a sample of 32 without replacement, what is the probability of two men being on the same team one year and then two years in a row?
1
vote
1answer
29 views

Envelopes and Mailboxes

We suppose $n$ and $p$ are two positive integers. A) In how many ways can you divide $p$ identical envelopes in $n$ mailboxes? (Each mailbox can hold several envelopes at the same time) B) In how ...
0
votes
1answer
20 views

Marble Probability

A bag contains 3 red marbles, 3 green ones, 1 lavender one, 6 yellows, and 4 orange marbles. How many sets of five marbles include either the lavender one or exactly one yellow one but not both ...
0
votes
0answers
28 views

Probability: Disease and Diagnosis

The probability of occurrence of a certain disease in a population is $1/101$. A diagnostic test has $9$ out of $10$ chances to detect the disease when the tested subject is actually affected. On the ...
1
vote
2answers
26 views

How do I calculate variance for sum of dice?

I'll post my work, but I'm not sure how to calculate variance. The question asks for the expected sum of 3 dice rolls and the variance. I think I got the expected sum. Any help would be awesome :) ...
2
votes
3answers
130 views
+100

Prove that there are two frogs in one square.

A certain chessboard is infinite in size. There is a frog sitting in the center of every square. After a certain time, all the frogs jump such that They may jump to any possible square in the ...
0
votes
1answer
40 views

Probability: put 20 distinct balls randomly in 12 urns

You put 20 distinct balls randomly into 12 urns. What is the probability of having 3 urns with 4 balls each and 4 urns with 2 balls each (the other 5 urns are left empty). For my sample space I have: ...
-2
votes
1answer
51 views

Finding $E[X^2]$ if $E[X] = \frac{\pi k}{4}$ [duplicate]

We try to approximate $\pi$ by choosing random points in a square and seeing if they lie within the inscribed circle. The probability that a point is in the circle is $\frac{\pi}{4}$. Suppose we ...
1
vote
1answer
35 views

Probability and Combinations

In a family with 6 children, a. What is the probability of having three children of each sex? b. What is the probability of having four of one sex and two of the other sex? I know in this problem ...
-2
votes
1answer
34 views

Selecting red and white balls [closed]

A box contains $4$ white and $3$ red balls if $x$ denotes the number of red balls in three draws with replacement. Find the probability distribution of $x$.
1
vote
3answers
94 views

How to prove that e^x is convex? [duplicate]

For convexity : $$e^{ta+(1-t)b} \leq t \cdot e^a+(1-t)e^b \Rightarrow e^{(a-b)^t} \leq te^{a-b} + 1 - t$$ Now I'm stuck on how to solve it further.
0
votes
1answer
26 views

Suppose we toss a coin 5 times and define Y as number of runs of heads. How do you find expectation and variance?

Range would be {0,1,2,3,4,5} Is there an easy way to find expectation rather than writing out all the possible outcomes?
-4
votes
1answer
121 views

Approximating $\pi$ using expected values [closed]

We approximate $\pi$ by choosing random points in a square and seeing what fraction fall in the inscribed circle. If we choose $k$ random points, the expectation $E[X]$ of the number $X$ of points in ...
1
vote
0answers
30 views

Simple problem in probability

You have 100 lightbulbs. Every lightbulb is either functioning or not. You test 20 of them, and all of the 20 are functioning. What is the probability that 10 of the 100 lightbulbs do not function? ...
2
votes
1answer
40 views

How do you handle this kind of probability?

What is the probability of selecting a singular matrix from $\Bbb{R}^{3\times 3}$? I calculated it to be zero based on their being approximately $9$ degrees of freedom to choose entries of $A$ such ...
1
vote
2answers
26 views

$K$ events that are $(K-1)$-wise Independent but not Mutually/Fully Independent

I had the following question: Construct a probability space $(\Omega,P)$ and $k$ events, each with probability $\frac12$, that are $(k-1)$-wise, but not fully independent. Make the sample space as ...
0
votes
1answer
19 views

How many functions defined on $n$ points are possible if each functional value is either $0$ or $1$?

How many functions defined on $n$ points are possible if each functional value is either $0$ or $1$? This is from the text A First Course on Probability by Sheldon Ross. The solution he ...
0
votes
2answers
25 views

Visualizing generalized basic principle of counting

The basic principle of counting states: Suppose that two experiments are to be performed. Then if experiment 1 can result in any one of m possible outcomes and if, for each outcome of experiment ...
4
votes
2answers
93 views

Green balls and Red balls, probability problem

I'm studying for my exam and I came across the following draw without replacement problem : ...
1
vote
1answer
48 views

How many random cards picks with replacement are required?

You pick 1 card from a standard deck of 52 cards. Then put it back in, and pick a card again. Then put it back in and pick a card. etc... How many times do you have to repeat in order to have ...
1
vote
1answer
26 views

Probability: 30 balls in a bucket, homework

i need some help with some homework, first time i am doing probability and statistics, id like to know if my 2 answers below are correct, and how i can solve the remaining 2. There are 30 balls in a ...
6
votes
6answers
347 views

Book on combinatorial identities

Do you know any good book that deals extensively with identities obtained using combinatorial and/or probabilistic arguments (e.g., by solving the same combinatorial or probability problem in two ...
0
votes
1answer
13 views

Throw 3 balls into 3 bins find range, distribution, and partition based on following information

There are 3 indistinguishable balls and 3 distinguishable bins. Let random variable X = #balls in bin 1 and random variable N = #occupied bins Range(X) = {0,1,2,3} Range(N) = {1,2,3} A0 = No balls ...
1
vote
2answers
56 views

Show how the probability that an 8 character password contains exactly 1 OR 2 integers is .630

A password is 8 characters long. Each character can contain 26 lower case or 26 uppercase letters or a integer from 0-9. What is the probability that an 8 character password contains exactly 1 OR 2 ...
1
vote
0answers
33 views

Minimum Number of Possible Combinations to Predict Results of Double-Outcome Events

There are "n" different events. Each event can result in two possible outcomes (ie Yes or No). You make a guess for each event and list this (ie YYNYYNN for 7 events). To guarentee to correctly guess ...
1
vote
2answers
199 views

How many balls here can't be in the bag?

A bag contains colored balls of which at least $90\%$ are red. Balls are drawn from the bag one by one and their color noted. It is found that $49$ of the first $50$ balls drawn are red. Thereafter ...
2
votes
0answers
72 views

A probability problem with multivariate Gaussian distribution

I am a computer science guy, not a mathematician so kindly excuse me if there is any ridiculous error in my problem description. I have two clusters $C_1$ and $C_2$ in a feature space spanned by $k$ ...
1
vote
1answer
28 views

What is the probability of picking $4$ balls out from the two bins?

Assume there are $2$ bins (bin $a$ and bin $b$ ), and each bin contains $n$ indistinguishable balls with $n>10$. The probability of picking $k$ ball from each bin is $p_k$, ($k\ge 0$). Then what is ...
0
votes
1answer
23 views

Stack of 20 cards. Distribute to 4 people randomly… What is the probability each person ends up with the same number of cards?

Stack of 20 cards. Distribute to 4 people randomly. Assume that each person does not have t be dealt the same number of card. What is the probability each person ends up with the same number of ...
1
vote
3answers
31 views

Probability that the second ball is red

n balls, each equally likely to be red or black, are added to a box containing one red ball. Given that the first ball withdrawn from the box is red, what's the probability that the second ball ...
1
vote
1answer
28 views

minimum number of repetitions in a string

I have a string of length $n$ from an alphabet $A$ with $s$ symbols. What is the probability of having at least $k$ equal characters? It does not seem a binomial, nor a $1-$... form, nor a bar and ...
0
votes
2answers
23 views

get a 'win' in even expriment

unfair coin give '$x$' in probability $p$ and '$y$' in ($1-p$). we toss it up until we get '$x$'. what is the probability that we get '$x$' in even tossing? I know that for even tossing we need ...
0
votes
0answers
20 views

Number of possible multisets of multisubsets (with constraints)

Let's say I have a multiset $s = \{1, 2, 3, 4, 5\}$ (in this example there are no repeats, but there could be for any arbitrary s) Here are some examples of what I mean by 'multiset of multisubsets' ...
0
votes
2answers
96 views

Probability binomial the

A fair coin is thrown ten times. Find the probability that more heads arise than tails? Hi guys my question is a binomial theorem one I know that I'm just finding it hard to know what goes where. I ...
1
vote
3answers
40 views

Probability of Head in coin flip when coin is flipped two times

Probability of getting a head in coin flip is 1/2. If the coin is flipped two times what is the probability of getting a head in either of those attempts? I think both the coin flips are mutually ...
0
votes
1answer
23 views

Probability of getting no worms in your box

I am trying to work out the below fabricated scenario: Boxes of apples are checked for worms one at a time, and the probability that a given box of apples has worms is $p = 0.1$, independently of ...
0
votes
1answer
38 views

How can I figure out the total solutions in this Combinatorics problem?

Imagine you have a sequence of cards, each having a unique set of features. Example features : letter (A, B, C), number (1, 2, 3), and color (Red, Green, Blue) Some example cards : A1Red, B1Blue, ...
4
votes
4answers
711 views

Fewest number of moves to win the game 2048?

I'm trying to figure out the fewest number of moves one could make to win the game 2048. In another thread, someone placed the figure at 520, but I'm wondering if anyone knows how to mathematically ...
0
votes
0answers
28 views

about probablity of a card game with replacement allowed

I am thinking of a card game using standard 52 card and randomly deal 5 cards as initial hand. It is easy to calculate the probability of each winning hand (straight, flush, full house, etc.) dealt to ...
1
vote
3answers
43 views

probabilty of getting one of each character

Kelloggs (the breakfast-foods company) and Nintendo (which owns the Pokemon franchise) have agreed to distribute Pokemon toys for free inside specially-marked boxes of Fruit Loops. Upon opening a ...
41
votes
6answers
12k views

Probability that random moves in the game 2048 will win

I have recently played the game 2048, created by Gabriele Cirulli, which is fun. I suggest trying if you have not. But my brother posed this question to me about the game: If he were to write a ...
1
vote
1answer
33 views

determining the size of a test bank given acceptable number of repeats

I have a question for a challenge that I'm trying to create - having some trouble quantifying the size of the challenge's test bank. 20 people are taking a challenge of 9 questions the test bank (n) ...