# Questions tagged [probability]

For basic questions about probability and for questions about calculating a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using [tag:measure theory]), ask under [tag:probability-theory] instead. For questions about specific probability distributions, use [tag:probability-distributions] instead.

75,857 questions
Filter by
Sorted by
Tagged with
2k views

### What is the probability that the coin drawn is fair

A box contains $n$ number of coins, $m$ of which are fair and the rest are biased. The probability of getting a head when a fair coin is tossed is $1/2$, while it is $2/3$ when a biased coin is tossed....
432 views

### Probability question about change in vending machines; maybe markov chain?

Suppose there are vending machine that sells its goods for $3$. It's known that a third of the buyers use three coins of $1$, a third of the buyers use $2$ and $1$, and the last third use $5$. The ...
2k views

### probability question related to pattern in coin tossing [closed]

If I toss a fair coin $n$ times, calculate the probability that no pattern HHTHTHH occurs.
806 views

### proof of equivalent definitions of recurrent states for Markov chains

I am wondering if anyone could prove the following equivalent definition of recurrent/persistent state for Markov chains: 1) $P(X_n=i,n\ge1|X_0=i)=1$ 2) Let $T_{ij}=min\{n: X_n=j|X_0=i\}$, a state $i$...
837 views

### 1-D Random walk expectation calculation

I need assistance with the following question: The particle starts from the origin on the number line . It makes n steps at total. At each step it jumps with the probability 1/2 to the origin and ...
122 views

### Probability homework question

There are 6 of x and 4 of y. A group of 5 is selected. What is the probability of there being 3x and 2 y? I completely forgot how to do this and my textbook doesn't have any information on it.
2k views

### Improper Random Variables

What is an Improper Random Variable? I know the definition in terms of the CDF like, F(∞) - F(-∞) <1. Could any one explain it more clearly, specifically I am looking for an example of an improper ...
2k views

### Probability of never reach -1 for a 1D random walk of n steps

On the number line, starting from 0. There is a probability of $p$ of moving 1 unit to the positive direction, and $1-p$ of moving 1 unit to the negative direction. What is the probability the walk ...
302 views

132 views

### Probability value in a skewed data

A question goes like this: Given that there 2 questions out of 3 questions to pass an exam and follow are details of number of people who attended the questions correctly, what is the maximum number ...
383 views

### Geometric distrubution and expectancy

I have following problem: We throw a fair dice time after time.What is time expectancy to get first time 66 i.e two six in the row for the first time. I probably should use this http://en.wikipedia....
1k views

### Bounding probability that sum of random variables deviates from expected value

I'm working on a problem that requires me to find an upper bound on the probability that the sum of independent draws from a random variable deviates from the expected value of that sum by more than a ...
769 views

2k views

### Going to the Movies!

I was looking at movie times today and was struck by the oddly-spaced showing times. For example, at the local Loew's Theater "Tron: Legacy 3D" (127 min.) is playing on two screens at the following ...