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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Approximating the result of probability

So, here's a question asked in an interview: 10 dices are rolled simultaneously. What is the probability of getting the sum of numbers appearing on top of all the dice as 35? If we calculate manually, I think it's pretty tedious with no…
Charlie
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A random walk on half the number line

Consider a symmetric random walk on the number line where steps are size $1$. If a step from $0$ tries to go to $-1$ you stay at $0$ instead. You start at $0$ and we want to compute the expected time to reach $x>0$. From numerical experiments it…
user35671
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Probability to draw specific ball from the bag as last one

Let's say I have a bag with 8 numbered balls inside, and I'm drawing them 1 by 1 until I get ball #1. What's the chance of me drawing ball #1 as last one? I was under the impression that the chances for me to draw it last is $$\frac18*…
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What is the probability of rolling 6 on two cubes when we only count the higher of the two numbers

We roll a six-sided die twice in a row and count the larger of the two different numbers. How likely is it to get a 6 this way? (This problem was translated and there isn't any additional information). I am very confused - firstly, I tried counting…
MaxE
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Probability of buying a defective laptop

There are two brand shops - A and B. A manufactures 1000 laptops, of which 100 are defective. B manufactures 100 laptops, of which 10 are defective. When I go to buy at a shop of any brand, they simply pick a laptop at random and give it to me.…
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Two biased coins. You pick a coin, flip it, and it lands heads. What is the probability it will be heads on the next flip?

You have a bag with two coins. One will come up heads $40\%$ of the time, and the other will come up heads $60\%$. You pick a coin randomly, flip it and get a head. What is the probability it will be heads on the next flip? My approach to the…
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What is the probability that the roots of $P(x) = \frac{1}{4} x^2 +Ux+V^2$ are real?

Assume that $U$ and $V$ are independent normally distributed random variables, each with mean $0$ and variance $1$. Find the probability that the roots of the polynomial $P(x) = \frac{1}{4} x^2 +Ux+V^2$ are real. This is a question I had to work…
Galois
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Intuition on independence of two events.

The following question is taken from a textbook: Stanley H. Chan: Introduction to Probability for Data Science, 2021. (pp. 87-88) Please note that this is not a question on how to calculate independence, I am fully aware of this. Instead, the…
nan
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Is it possible to partition $[a,b]$ into countably many "identical" sets which are translation from each other?

Given $[0,1]$, is it possible to find one set $A_1\subset[0,1]$ and $A_i = A_1 + a_i, i\in\mathbb{N}, a_i\in\mathbb{R}$ such that $\{A_i\}$ is a countable partition of $[0,1]$. By $A_1 + a_i$, it means translating $A_1$ by the value of $a_i$, e.g.…
L Q
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Two numbers are randomly selected from the set {0,1,2,3,4,5,6,7} without replacement

What is the probability that the sum of the two numbers is 7? [what i did] 0+7 1+6 2+5 4+3 my ans: 4/8 Is this right or wrong? Does without replacement mean we can't use the same number twice? IE: 4+2 AND 2+4? Thanks for the help
MethodManX
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One red, one green and one blue ball in a box

I asked myself a question about probabilities and got pretty confused about it. Let's say there is a box with 1 red ball, 1 green ball and 1 blue ball inside. I pick randomly a ball from the box, then put it back, and repeat the process two more…
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Probability that a 3-digit randomly chosen number is divisible by 5

$$\text{Set}\; = \{0,1,2,3,4,5,6\}$$ Find the probability that a three digit number which does not have the digit $0$ chosen at the far left and is chosen at random from the set, is NOT a multiple of 5. $$P(\text{NOT A multiple of 5}) =…
MethodManX
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Rolling a pair of six-sided dice, what is the probability that the larger number is at least 5?

You have two six-sided dice. What is the probability that the larger number rolled will be at LEAST 5? I have listed out all the possible rolls. You can set dice 2 equal to 5, and roll dice one. The possible rolls are (1,5), (2,5), (3,5), (4,5). Do…
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What is the probability one man is chosen for treasurer and one woman for secretary?

So everyone, I have a simple probability question that I cannot wrap my head around. It go like this: There are $6$ men $9$ women on committee. $2$ people are chosen for treasurer and secretary. What is the probability one man is chosen for…
Aiden Chow
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Quick ways for approximating $\sum_{k=a_1}^{k=a_2}C_{100}^k(\frac{1}{2})^k(\frac{1}{2})^{100-k}$?

Consider the following problem: A fair coin is to be tossed 100 times, with each toss resulting in a head or a tail. Let $$H:=\textrm{the total number of heads}$$ and $$T:=\textrm{the total number of tails},$$ which of the following events…
user9464