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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Expected number of tosses to get 3 consecutive Heads

I have a fair coin. What is the expected number of tosses to get three Heads in a row? I have looked at similar past questions such as Expected Number of Coin Tosses to Get Five Consecutive Heads but I find the proof there is at the intuitive, not…
RandomGuy
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Why is my intuition wrong that one of two archers win in a tournament?

The probability of Robin and Tuck hitting a target respectively are $0.45$ and $0.38$. For each round of the tournament, each archer must shoot simultaneously at their targets. A player wins the tournament if in a round, one archer hits the target…
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Expected number of steps to finish all the cookies

Please help on this question: Steve has 256 cookies. Each cookie has a label that is a distinct subset of $\{1,2,3,4,5,6,7,8\}$. At each step, Steve chooses a cookie randomly and eats it as well as all othe cookies whose label is a subset of the…
Kay K.
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Must probability density be continuous?

From other materials that I've read, the probability density of a continuous random variable must itself be continuous. Is this correct? If it is, I don't understand why that would be so, why can't the probability change abruptly?
Paul Manta
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A coin is flipped ten times. What is the probability that the first three are heads if an equal number of heads and tails are flipped?

I understand the question but I am not sure how to solve it. For example, if we flip HHHTTTTT then the next three must be heads because of the question. This however seems counterintuitive. I believe that there are $2^{10}$ possible strings, but I…
RS Evolve
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Expected number of steps before three counters reach N modulo 2N at the same time

We have three counters, $i, j, k$, all initialized to zero. Each step consists of adding or subtracting one from one of the counters, so $(\Delta i, \Delta j, \Delta k)$ is selected among $(\pm1, 0, 0), (0, \pm1, 0), (0, 0, \pm1)$, each with…
hakos
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Expected value of a non-negative random variable

How do I prove that $\int_0^\infty Pr(Y\geq y) dy = E[Y]$ if $Y$ is a non-negative random variable?
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How to calculate the probability of rolling 6 at least 5 times in a row, out of 50 tries?

If I roll the dice 50 times, how do I calculate the chance that I will roll 6 at least 5 times in a row? Why this problem is hard With 5 tries this would be easy: take $(1/6)$ to fifth power. With 6 tries this is manageable; take the probability of…
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how does expectation maximization work in coin flipping problem

joriki: Thanks for your answer regarding the expectation maximization work relating to the coin flipping problem ( how does expectation maximization work? ). You have explained how the probability of coin A or coin B are selected for each set of…
xuesong
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Can a probability density function take negative values?

From a textbook: Theorem 3.5. A function can serve as a probability density of a continuous random variable $X$ if its values, $f(x)$, satisfy the conditions^ $f(x)\ge0$ for $-\infty
Ahmed Ali
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P(tomorrow is the end of the world) =?

Here we have $3$ prophets alpha, beta, gamma, they all predict that tomorrow is the end of the world. It's known that the accuracy of alpha's and beta's prediction is $90\%$, while that of gamma's is $4\%$. What is the probability that tomorrow is…
JSCB
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Expected Sum of 30 sided die rolls

Roll a 30-sided die. Add up each consecutive outcome. Stop rolling when the sum >= 300. What's the most likely result of the sum?
QRIUS2KNW
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Probability of 20 consecutive success in 100 runs.

Suppose a chess player have a win rate equal 90%, what is the chance to have 20 consecutive wins (successes) playing 100 games? Consider that lose/draw = fail. I've studied basic statistics in college and it seems like a binomial distribution…
Anthony
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How many flips of a fair coin does it take until you get N heads in a row?

The question is pretty much in the title. How many flips of a fair coin does it take until you get N heads in a row on expectation? I am curious how this is proven in terms of probability (no this is not for homework, just genuine curiosity as it's…
user74918
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How to find $E(f(f(f(\ldots f(x)))$

I have a random function $f(x)$ which returns one of the integers in the range $[0, x-1]$ with equal probability and $f(0) = 0$. What is the expected value $E(f(f(f(\ldots f(x)))$ ($n$-times $f(x)$)? The answer should be a function of $x$ and $n$.
user65009
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