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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First to 1000 rolls wins

You and your friend each have a standard $6$-sided die with sides numbered $1, 2, \ldots 6$, every side has an equal probability of arising in a random roll. You throw the cube first* the number that land, is the amount of times your friend need…
TuYu
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Exercise with a dice with 14 faces

I'm having trouble solving this problem: There's a dice with 14 faces, of which 6 are squared, and 8 are triangular. If the probability of getting a squared face is twice the probability of getting a triangular one, then what is the probability of…
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Calculating the probability mathematically

A football player's performance is recorded as 'well' or 'bad'. The probability of the football player performing well after the day he performed well is $3/4$. The probability of him performing bad after the day he performed bad is $1/2$. Given…
Andy
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Roll two fair six-sided dice and adds the results

Grace rolls two fair six-sided dice and adds the results. She than draws a square that has her result as the length of the diagonal. What is the probability that the numerical value of the area of her square will be less than the numerical value of…
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Show that two random variables are independent

I'm learning probability and need help with the following problem : Let $X_1, X_2$ be independent and identically distributed random variables with probability density function $$f(x_i) = \begin{cases} \lambda_i e^{\lambda_i x_i}, & x_i > 0 \;\;…
user347616
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Which one of the following is correct?

In an examination $30 \%$ of the students failed in Mathematics, $15 \%$ of the students failed in English and $10 \%$ of the students failed in both Mathematics and English. A student is chosen at random. If he failed in English then the…
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Which player is most likely to win when drawing cards?

Two players each draw a single card, in turn, from a standard deck of 52 cards, without returning it to the deck. The winner is the player with the highest value on their card. If the value on both cards is equal then all cards are returned to the…
DMA57361
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Probability that one random number is larger than other random numbers

Suppose you have several sets of numbers, each with a normal distribution. For each set, you know the standard deviation and mean. Now, if you independently choose one random number from each set, what is the probability that the number chosen…
dtlocke
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Is $c+Y$ lognormal?

Let $Y$ be a lognormal random variable and let $c>0$ be a constant. Is $c+Y$ lognormal? My attempt: We need to check if $X=\log(c+Y)$ is a normal random variable. Let $F_X$ denote the cumulative distribution function of $X$. Since $Y$ is lognormal,…
Siddhartha
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Applied Probability- Bayes theorem

I need help in all things related to identifying, defining conditions and solution feed back and reasoning most importantly. 1) A blood test indicates the presence of a particular disease 95 % of the time when the diseases is actually present. The…
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If a student is absent twice, then what is the probability that the student will miss at least one test?

The probability that a teacher will give an unannounced test during any class meeting is 1/5 . If a student is absent twice, then the probability that the student will miss at least one test is ...? Answer given : 9/25 My attempt: Let $G$:…
Arishta
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What are chance of two randomly generated 4 digit strings being the same?

I am building a website where an alphanumeric ID will be generated. As of now, I have it randomly grabbing a number or letter from this data set: ABCDEFGHIJKLMNOPQRSTUVWXYZ 0123456789 So there are 36 possibilities. If my math is right, if I make…
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Probability of decreasing random structures

Given that we have $N$ consecutive structures that can have a maximum height of $H$, where the individual height $h_i$ depends on random coin flips (for each structure, an additional height has a probability of 0.5. The probability is given by…
David
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How do you sum PDF's of random variables?

I have a question asking me to determine the PDF of $L=X+Y+W$, where $X$, $Y$ and $W$ are all independent. $X$ is a Bernoulli random variable with parameter $p$, $Y \sim \mathrm{Binomial}(10, 0.6)$ and $W$ is a Gaussian random variable with zero…
Hoser
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what is the expected maximum number of balls in the same box

If I have $m$ distinct boxes, and $n$ distinct balls. I put all of these balls into the boxes with one box possibly containing more than one balls. What is the expected maximum number of balls in one box? Appreciate your thoughts on solving this…
Qiang Li
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