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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how to find probalility that a student misses at least one test if he/she is absent twice?

The probability that a teacher will give an unannounced test during any class is $\dfrac15$. If a student is absent twice then probability that he/she misses at least one test is $\\ \hspace{5cm}$ a) $\dfrac23\ \quad $ b) $\dfrac45\ \quad$c)…
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How to calculate this probability

First, if this question is too basic for math.stackexchange, I apologize. I wasn't sure where else to ask, but if you have a suggestion I'll happily take the question elsewhere. I'm totally mathematically unsophisticated, and I was asked a…
Andrew
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Probably that an $80\%$-truthful person actually rolled a $6$

A person, $A$, speaks the truth $4$ out of $5$ times. The person throws a die and reports that he obtained a $6$. What is the probability that he actually rolled a $6$? I know there is a similar question like this but my doubts are different from…
user501655
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Average number of flips for someone to win?

You and I each have 14 dollars. I flip a fair coin repeatedly; if it comes up heads I pay you a dollar, but if it lands tails you pay me a dollar. On average, how many times will I flip the coin before one of us runs out of money? I know that the…
user45220
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Sum of 2 dice rolls is even - probability

i have to calculate how probably it is, that the sum of 2 dice rolls is even. From my course i know that i have N^n Possibilities = 6^2 = 36. 6 = sides of dice and 2 = number of dice rolls Know i calculated the possibilities for all even values. P =…
hukachaka
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Expected number of trials to see x unique values out of N total values

I'm new to these forums so please forgive me if my question is poorly worded/phrased. Suppose I have a list of N unique integers that I'm drawing from, one at a time, with replacement. Let x be the number of non-repeated integers I've drawn thus far…
Billy
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What's the expected value of a lottery ticket?

Suppose there's a lottery. Each ticket sold has probability $p$ of winning, and they are all independent of each other. The size of the jackpot is $j$. If there are $n$ winners, each winner gets a payoff of $j/n$ dollars. The total number of tickets…
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Coin Tossing Game Optimal Strategy Part 2

I recently asked a question, that was answered excellently: Coin Tossing Game Optimal Strategy Here I'd like to complicate the question slightly. This part stays the same: You start off with £100 and you toss a coin 100 times. Before each toss you…
Boris
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Probability question about "good" tickets.

The problem: Out of 20 exam tickets, 16 tickets are "good". Tickets are carefully mixed, and students take turns pulling one ticket. Who has the better chance to draw a "good" ticket the first or the second student in the queue? My attempt:…
Nick202
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simple probability question about mutually exclusive event

If $P(A) = 1/3$ and $P(B^{\complement}) = 1/4$, then, can $A$ and $B$ be mutually exclusive? I already know that for $A$ and $B$ to be mutually exclusive, $A \cap B = \varnothing$ and $P( A \cup B ) = P (A) + P(B)$. I just can't proceed further…
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The probability of hitting equally distanced mines on a straight line

Recently I was given the following problem. Anti-tank mines are placed on a straight line 15 meters apart from each other. The tank, 3 meters wide, runs perpendicular to this line. What is the probability that the tank will hit a mine. My problem…
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Group Russian Roulette

This problem is from "Mathematical Puzzles: A Connoisseur's Collection" (P. Winkler, AK Peters, 2005) as the opening puzzle in the chapter "Probability". There are N armed people. At each chime of a clock everyone spins around and shoots a random…
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Problem with two loaded die and the probability to get a sum greater than 10 knowing the outcome of one die

I face the following problem but disagree with the solution that has been provided to me: You throw two times a loaded die such that $P(1)=P(3)=P(4)=P(5)=1/8$ and >$P(2)=P(6)=1/4$. One of the dice gave 6 (but we don't know which one). What is the…
Bardamu
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Probability of center of unit sphere contained within a random tetrahedron

Randomly select 4 points on the surface of a unit sphere and then construct an inscribed tetrahedron (triangular pyramid) containing the random points as vertices. What is the probability that the center of the sphere is contained within the…
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Time to find first copy of a duplicate

Consider a random process which samples uniformly with replacement from [n]. The expected time to find a duplicate is a constant factor times $\sqrt{n}$. This is a version of the famous Birthday Problem. How can one find the expected time to find…
Willem
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