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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Multiple-choice question about the probability of a random answer to itself being correct

I found this math "problem" on the internet, and I'm wondering if it has an answer: Question: If you choose an answer to this question at random, what is the probability that you will be correct? a. $25\%$ b. $50\%$ c. $0\%$ d. $25\%$ Does this…
user11088
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In Russian roulette, is it best to go first?

Assume that we are playing a game of Russian roulette (6 chambers) and that there is no shuffling after the shot is fired. I was wondering if you have an advantage in going first? If so, how big of an advantage? I was just debating this with…
nikkita
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What's 4 times more likely than 80%?

There's an 80% probability of a certain outcome, we get some new information that means that outcome is 4 times more likely to occur. What's the new probability as a percentage and how do you work it out? As I remember it the question was posed like…
Jim
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What is the difference between independent and mutually exclusive events?

Two events are mutually exclusive if they can't both happen. Independent events are events where knowledge of the probability of one doesn't change the probability of the other. Are these definitions correct? If possible, please give more than one…
Adnan Ali
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probability $2/4$ vs $3/6$

Recently I was asked the following in an interview: If you are a pretty good basketball player, and were betting on whether you could make $2$ out of $4$ or $3$ out of $6$ baskets, which would you take? I said anyone since ratio is same. Any…
zephyr
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How to generate a random number between 1 and 10 with a six-sided die?

Just for fun, I am trying to find a good method to generate a random number between 1 and 10 (uniformly) with an unbiased six-sided die. I found a way, but it may requires a lot of steps before getting the number, so I was wondering if there are…
P.A.
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What is the chance to get a parking ticket in half an hour if the chance to get a ticket is 80% in 1 hour?

This sounds more like a brain teaser, but I had some kink to think it through :( Suppose you're parking at a non-parking zone, the probability to get a parking ticket is 80% in 1 hour, what is the probability to get a ticket in half an hour? Please…
Rock
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There are 4 cups of liquid. Three are water and one is poison. If you were to drink 3 of the 4 cups, what is the probability of being poisoned?

In Season 5 Episode 16 of Agents of Shield, one of the characters decides to prove she can't die by pouring three glasses of water and one of poison; she then randomly drinks three of the four cups. I was wondering how to compute the probability of…
student
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Average Distance Between Random Points on a Line Segment

Suppose I have a line segment of length $L$. I now select two points at random along the segment. What is the expected value of the distance between the two points, and why?
Kenshin
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If we randomly select 25 integers between 1 and 100, how many consecutive integers should we expect?

Question: Suppose we have one hundred seats, numbered 1 through 100. We randomly select 25 of these seats. What is the expected number of selected pairs of seats that are consecutive? (To clarify: we would count two consecutive selected seats as a…
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What's the probability that a sequence of coin flips never has twice as many heads as tails?

I gave my friend this problem as a brainteaser; while her attempted solution didn't work, it raised an interesting question. I flip a fair coin repeatedly and record the results. I stop as soon as the number of heads is equal to twice the number of…
Elliott
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The two-daughter-problem

When hearing about the two-daughter problem, I first thought it to be quite clear (after, of course, at first falling into the trap like many of us), but on the second glance, I encountered some serious problems with my understanding. The original…
Thern
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Expected Number of Single Socks when Matching Socks

Whenever I go through the big pile of socks that just went through the laundry, and have to find the matching pairs, I usually do this like I am a simple automaton: I randomly pick a sock, and see if it matches any of the single socks I picked out…
Bram28
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Odds of winning at minesweeper with perfect play

How would someone go about doing this? Assume that the first "click" will never be a bomb, and that the number of mines and the area are both known. Rather hoping there is a clever way to do this, but I will not be so surprised if there…
soandos
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What is the chance that a rabbit won't fall off a table if you put it somewhere and it moves.

If you would put a rabbit randomly on a circular table with radius $r= 1$ meter and it moves $1$ meter in a random direction, what is the chance it won't fall off? I tried to do this using integrals, but then I noticed you need a double integral or…
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