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Questions tagged [probability]

For questions about probability. independence, total probability and conditional probability. For questions about the theoretical footing of probability use [tag:probability-theory]. For questions about specific probability distributions, use [tag:probability-distributions].

The probability that an event occurs is a number in the interval $[0, 1]$, which represents how likely the event is to happen. $0$ indicates it will never happen, $1$ indicates it will always happen.

For example, throwing two dice gives a total of $6$ five times out of thirty-six. We write $$P(X=6)=\frac{5}{36}$$.

Use this tag for basic questions about probability, independence, total probability and conditional probability.

For questions about the theory of probability, use instead. For questions about specific probability distributions, use .

105859 questions
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Correlation Coefficient between these two random variables

Suppose that $X$ is real-valued normal random variable with mean $\mu$ and variance $\sigma^2$. What is the correlation coefficient between $X$ and $X^2$?
Julie
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What is the probability that $HH$ occurs before $TH$ in an infinte sequence of coin flips?

This is one of the questions of a set of exam review questions that don't have solutions to them. I can't get my head around this but it seems so simple. By flipping a fair coin repeatedly and independently, we obtain a sequence of H's and T's.…
Roman
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Conditional Entropy is less than entropy

Let $p_{ij}=P(X=i,Y=j)$ be the joint distribution, $P(X=i)=p_i=\sum_j p_{ij}, P(Y=j)=q_j=\sum_i p_{ij}$ be the marginal distributions, and $p_{i|j}=\frac{p_{ij}}{q_j}$ be the conditional distribution. Then the conditional entropy is defined as…
bret
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What are the odds of rolling a 3 number straight throwing 6d6

If you throw six fair dice, what are the odds that at least three dice make a straight (i.e. 123, 234, 345, or 456) I am certain that I am making a mistake in calculating it?
user1873
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What is the actual meaning of runs in terms of coin tossing?

I am not able to understand the concept of runs in terms of coin tossing. As per my question, suppose a coin is tossed x times, then we have to find the expected number of runs. But, what is a run? Can anybody give a detailed example? As per the…
Ambidextrous
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Probability based on Hamming distance

Two $n$ bit binary strings $S_1$ and $S_2$ are chosen randomly with uniform probability. The probability that the Hamming distance in between these strings (the number of bit positions where the two strings differ) is equal to $d$ is: $\binom{n}{d}…
Rishi Prakash
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An inequality about binomial distribution

The question is: Consider $n$ Bernoulli trials, where for $i = 1, 2,..., n$, the $i$th trial has probability $p_i$ of success, and let $X$ be the random variable denoting the total number of successes. Let $ p \ge p_i$ for all $i = 1, 2, \ldots ,…
NonalcoholicBeer
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Probability of balls in the box

In a box there are 12 balls; 4 defective, 8 not defective. What is the probability that when 3 balls are drawn, at least two of them are defective. I know the answer is $$\frac{{4 \choose 2}{8 \choose 1} + {4 \choose 3}}{{12 \choose 3}}$$ But why…
Kraken
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Probability of 100 coin tosses

I was wondering if I could get some help on this problem. Suppose that a fair coin is tossed 100 times. Find the probability of observing at least 60 heads. Thanks! Note: on the study guide I did "1-binomcdf(100,0.50,59)" and still got it…
Garrett Simon
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Infinite Probability

A has 2 dollars and B has 3 dollars. They toss a coin. If it is heads A gives 1 dollar to B, B gives 1 dollar to A otherwise. P(Heads) = 1/3 What is the probability of B's winning? I tried too much but I could not solve this. I found P(B) = {HH,…
g3d
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Probability of getting red ball at ith step

An urn has r red and w white balls that are randomly removed one at a time. Let $R_i$ be the event that the $i$th ball removed is red. Find $P(R_i)$ I started with calculating $P(R_1) = \frac{r}{r+w}$. Next, $$P(R_2) = P(R_2|R_1)\cdot P(R_1)…
Yal dc
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Probability game with three players winning plus losing doesn't equal 1

I have a game of cards numbered 1-10. Three players draw cards, the highest card wins. Cards are not replaced. The first player draws a 9. I want to work out the probability of that player winning and losing. The probability of winning is the…
Liath
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What is the probability of picking $3$ $A$'s, $4$ $B$'s, $5$ $C$'s and $8$ $D$'s when you pick $20$ balls?

Q: Choose $20$ balls from an urn with infinite numbers of balls. The balls are labeled with $A, B, C, D$ and each has $25$% of chances getting picked. What is the probability of picking $3$ $A$'s, $4$ $B$'s, $5$ $C$'s and $8$ $D$'s when you…
jamesclyeh
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What is the probability that the square $U$ is inside the square $S$

Given a square $S$ with size $1 \times 1$. Two randomly selected points $A$ and $B$ are inside the square. Let $U$ be a square with diagonal $AB$. How to find out the probability $P$($U$ is inside $S$).
Xpast
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Estimating the average number of passengers in cars in a parking lot.

All the workers at a certain company drive to work and park in the company’s lot. The company is interested in estimating the average number of workers in a car. Which of the following methods will enable the company to estimate this quantity?…
srodriguex
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