# Questions tagged [elementary-probability]

The tag has no usage guidance.

58 questions
Filter by
Sorted by
Tagged with
23 views

### Probability of event A and B

Consider a events A (Man passes in exam A) P(A)=0.7 Event B (Man passes in exam B) P(B) =0.8 Let's take that exams are not related to each other and thus events are independent. Then what is the ...
15 views

42 views

### 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 ...
34 views

### Conditional probability question about children

Sushma has $2$ children. Let $A$ be the event that the oldest child is a girl, $B$ be the event that at least one child is a girl, and $C$ be the event that both children are girls. Which of the ...
20 views

### Coin flips; heads and two tails percentages [closed]

I have some simple rules and want to compute the probability either as a real number or as percentage of the outcomes. Say someone flips a coin, and there is $50$/$50$ chance or equal probability it ...
82 views

131 views

### Finding the expected value of a variable using double integration in polar coordinates.

This is a statistics problem, but it requires integration. And I'm getting a little lost in the problem because there are multiple variables involved when you switch over to polar coordinates, and I ...
19 views

### Probability Distributions $P(A^c\cap B^c)$? [closed]

How can i do this distribution from Pitman probability textbook? I dont know how this expands. Do i use the compliment rule? Difference rule? Inclusion-exclusion?
24 views

### Given a probability $p$, what is the upper bound of how many columns in a row-stochastic matrix exceed $p$?

Given a probability $p$ and a row $i$ of a stochastic matrix $M$, what is the maximum number of columns $j$ such that $M_{ij} \gt p$? ...
73 views

### 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(...
53 views

### probability problem solution with full proof [closed]

n+4 apples are distributed at random among n persons. Find the probability that atleast one of them will receive none. I want a detailed solve using complex combinatorial summation. Please help me to ...
39 views

### Conditional probability as a function

Sample space (S) is a set of all possible outcomes of a random experiment. $S = \{x | x$is an outcome$\}$ Event (E) is a subset of sample space. $E \subseteq S$ Probability is a function from ...
30 views

### Probability of Random Selection [duplicate]

Fifteen coupons are numbered 1 to 15. Seven coupons are selected at random, one at a time with replacement. What is the probability that the largest number appearing on a selected coupon be 9? My ...
23 views

### Probability that the drawn ball is the only ball of its kind.

A bag contains 7 balls of any colour. A ball is drawn at random and is found to be of blue colour. Find the probability that it is the only blue coloured ball. I am not getting a start. Like do we ...
91 views

### Three six-sided dice are rolled. Denote the greatest value rolled to be x and the smallest value rolled to be y. What is the expected value of x-y?

Three six-sided dice are rolled. Denote the greatest value rolled to be $x$ and the smallest value rolled to be $y$. What is the expected value of $x-y$? Any help is greatly appreciated. I'm not sure ...
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 ...