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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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Determining the number of balls in a box

I'm facing problems solving this question and I'd like some help: A box contains n balls, where just 2 are white and the rest are red. A random sample of 4 balls is drawn without replacement. It's known that the probability of the 2 white balls are…
Rods2292
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Finding $E(N)$ in this question

suppose $X_1,X_2,\ldots$ is sequence of independent random variables of $U(0,1)$ if $N=\min\{n>0 :X_{(n:n)}-X_{(1:n)}>\alpha , 0<\alpha<1\}$ that $X_{(1:n)}$ is smallest order statistic and $X_{(n:n)}$ is largest order statistic. how can find…
hadisanji
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Two tower problem

Suppose that we have two towers of equal height $N$, each tower consisting of $N$ coins piled on top of each other. Now suppose we have a machine or whatever that takes a coin from one of the towers and move it to the other one. That is, a coin can…
Boazobargi
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Exponential Distribution - memoryless

A post office has 2 clerks. Alice enters the post office while 2 other customers, Bob and Claire, are being served by the 2 clerks. She is next in line. Assume that the time a clerk spends serving a customer has the Exponential(x) distribution. (a)…
user1489975
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What is a probability that at 2nd turn you will pick green ball?

I have an interesting question that I certainly don't know how to solve it. I've already read many topics on probability, eg: Probability that someone will pick a red ball first? and Comparing probabilities of drawing balls of certain color, with…
Tilqur
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Median from probability generating function

How can I find a median, or an approximation of a median, from the probability generating function?
Mile
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Flipping 100 coins and getting all heads.

I hold 100 fair coins in my hands. Then, I toss the 100 coins high into the air all at once. I understand that the chance of getting 100 heads when they land is 1 in 2 exp 100. Can someone help me determine, on average, how many attempts at tossing…
Eyost
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Independent events and Dependent events

I have a question regarding these strikingly similar problems with contradicting solutions. This is somewhat long, so prepare Probblem 1 Consider a bag of ten coins, nine are fair, but one is weighted with both sides heads. You randomly select a…
Lemon
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Difference between population, sample and sample value.

I was going through a book and reached a point where the author is comparing a Population, Sample and Sample Values. I don't seem to understand the difference at all. (Caps are Random Variables, small font are values/data points) What is the role…
Inquest
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random walk on the nonnegative integers

Consider a simple random walk on the integers with a reflecting barrier at $0$. What is the expected time the walk spends in the set $\{0, \ldots, k\}$ in the first $n$ steps? I'm curious about how the answer scales with $n,k$, and don't really…
angela o.
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Minimize the probability of getting the same sum of two rolls.

If you can design two dice that not necessarily fair and not necessarily weighted in the same manner, then roll twice. How can you minimize the probability of getting the same sum of the two rolls? My thought is since the probability of rolling the…
jacky123456789
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Expected Grade on Strange Testing Scheme

A teacher wants to give a test for a class. She gives the students 12 problems to study, 8 of which will be on the test. Students can pick 4 questions to answer and only those will be graded. If a student memorizes the answer to k problems, what is…
Ecclesiastic
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$3$ identical Dice are tossed simultaneously, The probability that all dice shows same number.

If $3$ identical Dice are tossed simultaneously, The find probability that all dice shows same number. $\bf{My\; Try::}$ Let $A$ be the event in which upper face of all dice shows same number and $S$ be the sample space Now Here we have $3$…
juantheron
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If $3$ married couples are seated randomly in a row, then find the probability that exactly $2$ couples can sit together.

If $3$ married couples are seated randomly in a row, then find the probability that exactly $2$ couples can sit together. My attempt is like this: $$\frac{4!(2!)^2}{6!}$$ My understanding: The probability of $3$ couples ($6$ people) sit in a row is…
Andrew Pang
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Expected value of a coin toss

You flip a coin. If you get heads you win \$2 if you get tails you lose \$1. What is the expected value if you flip the coin 1000 times? I know that the expected value of flipping the coin once is $\frac{1}{2}(2) - \frac{1}{2}(1) =0.50$ Would the…
johnbowen
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