Questions tagged [elementary-probability]
65 questions
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Car Convoy Problem
Cars travel down a one-way single-track road. The nth driver would like to drive at speed $V_n$ , where $ V_1,V_2, ..., V_n$ are iid random variables. Cars will get bunched into convoys. If $V_2>V_1>V_3$ , then the first convoy will consists of cars…
5
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3 answers
How to label the events in a probability problem?
I'm starting a statistics and probability class and it's still pretty hard for me to "name" my probability events, which I think makes it very difficult to solve problems.
I'll pick an example from my exercises to illustrate my problem :
We asked…
IEatBagels
- 153
5
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3 answers
Basic probability question- multiplication rule
I came across the following question in a textbook (bear in mind that this is the only information given)-
There is a $50$ percent chance of rain today. There is a $60$ percent chance of rain tomorrow. There is a $30$ percent chance that it will…
user468756
- 51
4
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1 answer
Simple combinatorics and probability theory related question
5 apples are randomly distributed to 4 boxes. We need to find probability that there are 2 boxes with 2 apples, 1 box with 1 apple and 1 empty box.
I'm getting the correct answer with $\frac{\frac{5!}{2!2!1!0!} * 4 * 3}{4^5} = 0.3515625$ (anyway,…
m73
- 43
4
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1 answer
Probability remains same Why?
A box has $m$ black and $n$ white balls. A ball is drawn at random and put back with $k$ additional balls of the same colour as that of the drawn ball. Now a ball is drawn again. Find the probability that it is a white ball.
I got the answer…
Maths_Rocks
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4
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Basket with Lilies and Roses. Find the number of roses.
Ques:
A covered basket of flowers has some lilies and roses. In search of rose, Sweety and Shweta alternately pick
up a flower from the basket but put it back if it is not a rose. Sweety is 3 times more likely to be the first one
to pick a rose. If…
CodeBlooded
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Notation regarding random variables
Let X be a random variable.
Consider X ~ F. It can be read as X has distribution F.
What is distribution referring here? Consider the following interpretations
1) If X is continuous, then F is a probability density function and if X is discrete then…
hanugm
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3
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Probability of seeing all numbers when rolling dice $7$ times
What is the probability when rolling a fair dice $7$ times to see every number $1, \dots, 6$ at least once?
My attempt: The total number of outcomes is $6^7$. Now we count the number of possibilities to see all the $6$ numbers as follows:
Let's…
user7802048
- 1,285
3
votes
2 answers
Expected value if two coins are drawn simultaneously from a bag containing $2$ one unit and $3$ two units of money
This is a question from the Resonance DLPD Algebra book (Page 250). To quote the book:
From a bag containing $2$ one rupee and $3$ two rupees coins, a person is allowed to draw $2$ coins simultaneously; find the value of his expectation.
My…
user69284
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Probability that two random numbers have a Sørensen-Dice coefficient over a given threshold
The following problem came up at work and my probability knowledge isn't up to the task. Let $a, b \in \mathbb{Z}_{2^n}$ be two $n$ bit integers. Their Sørensen-Dice coefficient is the quantity
$$
DS(a, b) = \frac{2|a \wedge b|}{|a| + |b|}
$$
where…
Hamish
- 795
3
votes
1 answer
Square Root of a Characteristic Function.
For any $\phi$ a characteristic function, is there a characteristic function $\Phi$ such that $\Phi ^2=\phi$?
I know that if $\phi$ is a characteristic function, then $\phi ^2$ is as well.
Also that $\sqrt{|\phi|}$ is not always a characteristic…
J.Summer
- 157
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1 answer
Proofs that impossible event B has NO conditional probability $\mathbb{P}(A|B)$. Is everything correct?
"$A$" is an event that has probability somewhere in interval $(0,1)$.
"$B$" is an event that has probability equal to zero.
Given that, I will prove that $\mathbb{P}(A \mid B)$ doesn't exist.
The first proof is based on reasoning alone:…
KarmaPeasant
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Does $\{\} = \{\{\}\} \cup \{\{\}\} \cup \cdots \cup \{\{\}\}$
Does any finite set $S = \{a, b, ..., c\}$ equal the union of it's elements? I believe so, but would I write that like
$$S = \{a\} \cup \{b\} \cup \cdots \cup \{c\} \tag{A}$$
$$\text{vs} $$
$$S = a \,\cup \,b \cup \cdots \cup c \tag{B}$$
Because I'm…
Zduff
- 4,380
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3 answers
What is the chance that a 1 in 1000 event will happen within the first 500 tries?
Say you have a thousand-sided die. You win if the die lands on 27, so a one in one thousand chance. I was curious as to what the chances are of winning if you roll the die 500 times. My gut told me that the odds were in your favor. I computed…
thumbtackthief
- 134
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0 answers
A question related to Probability(read body)
Q. Out of 100 students two sections of 40 and 60 students are to be formed. If Jack and Jenny are among the 100 students, what is the probability that:
a) they end up in the same section?
b) they end up in different sections?
I calculated the answer…
Aura Sartori
- 53