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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 .

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Probability of streaks

I thought of this question lately, but I'm not satisfied with the answer I got: If I flip a coin 100 times, what is the probability that I will get a streak of at least ten of the same side? The way I thought of solving it was just: $\left(90 \times…
user1546083
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Bank vaults and probability

A burglar breaks into a bank with the intention to open the vaults and steal some gold coins. He knows that each vault contains a number of 1 to 100 such coins with equal probability for each number. Since he is what we call an “ethical burglar”,…
Marius Stephant
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Guessing the probability by results of just 1 experiment

I have a probability question that seems easy, but I somehow can't wrap my head around it. Suppose we have a coin. Probability that coin toss will come out heads is some unknown value X. First toss came out as heads. What would you be your best…
Scorpil
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Cube and unit cubes

Consider a $3\times 3\times 3$ cube consisting of smaller $1\times 1\times 1$ unit cubes. The big cube is painted black on the outside. Suppose we disassemble the cube and pick a random unit cube, look at only one face and see it is black, without…
Sal.Cognato
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Intuitive idea of Expectation of random variable?

I'm studying probability for preparing myself for machine learning. I came across this notion of Expectation of (random variable) or (function of random variable) like $E[X]$ or $E[g(X)]$. Can anybody explain me the intuitive idea of the above…
amitlan
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Two players pick cards from standard 52 card deck without replacement...

I am struggling with this interview prep question... SOS Two players pick cards from standard 52 card deck without replacement: 1st player picks a card, then 2nd, then again 1st, then 2nd etc. They stop once somebody picks a king (of any suit), the…
user1029102912012
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How do we understand 6 people trying something is not 6 times the success rate?

Let's say if a task has a success rate of $20\%$, or $0.2$, meaning if a person tries it, then there is a $20\%$ chance he can succeed. One example is, if we generate a random number from 1 to 10, and getting the number 9 or 10 is considered to be a…
nonopolarity
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Prove $E[XY]=E[YE[X|Y]]$

Prove $E[XY]=E[YE[X|Y]]$. I tried proving it using the definition of covariance, but I ended up going in a circle. Any hints on how to go about the proof?
hello888
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Probability it rains

The probability it rains on Wednesday this week is 40%, while the probability it rains on Thursday this week is 30%. However, it is twice more likely to also rain on Thursday, if it has already rained on Wednesday. What is the probability it rains…
Marius Stephant
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fair value of a hat-drawing game

I've been going through a problem solving book, and I'm a little stumped on the following question: At each round, draw a number 1-100 out of a hat (and replace the number after you draw). You can play as many rounds as you want, and the last number…
user8364
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Confusion with regards to the phrase "exactly one of the events occurs"

Suppose we have events $A$ and $B$. We want to write the probability that exactly one of the events $A,B$ occurs in terms of $P(A),P(B)$ and $P(A \cap B)$ only My thought: Since I want only one occurring, $A$ or $B$, we must find $P(A \cup B)$…
user547160
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Two random variables and their sum

$X$ and $Y$ are random variables uniformly distributed on $[a,b]$. Could the random variable $Z=X+Y$ be uniformly distributed if $X$ and $Y$ are dependent and correlation between them doesn't equal $1$ or $-1$?
Xxx
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Probability of rolling a double $6$ with two dice

Two dice (with numbers 1 to 6 on the faces) are rolled. One die rolls a 6. What is the probability of rolling a double 6? One solution is to say that P(2 sixes) = $\frac{1}{6}$ since the first die gives a 6, so the only way to get a double six is by…
1123581321
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The probability that A hits a target is $\frac14$ and that of B is $\frac13$. If they fire at once and one hits the target, find $P(\text{A hits})$

The probability that A hits a target is 1/4 and the probability that B hits a target 1/3. They each fire once at the target. If the target is hit by only one of them, what is the probability that A hits the target? I know that this is an independent…
pyuntae
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Probability that $x^2-y^2$ is divisible by $k$

Let two numbers $x$ and $y$ be selected from the set of first $n$ natural numbers with replacement(i.e. the two numbers can be same).The question is to find out the probability that $x^2-y^2$ is divisible by $k\in \mathbb{N}$ For $k=2$ Any number…
Navin
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