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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What is the probability to get more heads in n-1 tosses than in n tosses ? (fair coin)

My approach so far is as follows: If $X_{n-2}$ is the number of heads in $n-2$ tosses then $E[X_{n-2}] = \frac{n-2}{2}$. So up to the $n-2$ toss it is all the same regardless if we end our experiment in $n$ or $n-1$ tosses. Then if we want to…
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Conditional independence property: weak union

Let $(X,Y,W,Z)$ be disjoint sets of random variables each with finite space. Then prove that if $\Pr(X\mid W,Y \cup Z)=\Pr(X\mid W)$ then $\Pr(X\mid Y,Z \cup W) = \Pr(X\mid Z \cup W)$. This is sometimes referred to as weak union in conditional…
user42574
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What's the difference between the probability of the nth coin flip, vs. the probability of flipping all the coins and getting one outcome

So this is more of a problem with getting an intuitive understanding. I'm sure something like this has been asked before but I couldn't find it because I didn't have a clue what my problem was to start with. Here goes: Question: You have flipped a…
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What are the odds of sitting next to the same person on two flights?

My wife left on a business trip this morning. 20 people from the same company caught two consecutive flights. Each person checked in independently, yet my wife ended up sitting next to the same colleague on both flights! What are the odds? Assume…
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probability that 5 square lie along a diagonal line

If $5$ squares are chosen at random from a chess board, what is the probability that they lie on a diagonal line?
juantheron
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Giving 1 apple to 1 of 3 children fairly with a coinflip

I wish to give an apple to 1 of 3 children fairly using a coin flip game. Each child calls heads or tails, and I flip the coin once for each child. If exactly one child calls correctly, that child gets the apple. If there is no one who calls…
Zhulu
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Game probability math question

Hi I need help with problem related to probability. There is a game of basketball between you and one other person. (only 1 game). Both agree that the stake will be $\$10$ (winner gains $\$10$ more, loser loses $\$10$). At a random point in…
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How many cards out of a standard deck would you need to draw to ensure two of them are different suits?

I believe that we are determining, in a worst case scenario, how many cards must we pick to draw a two different suit. My thought process is that we must get rid of all 13 cards to deplete an entire suit before we would be able to ensure the next…
Jlee
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Simple problem on conditional geometric probability

The occurrence of the event $A$ is equally likely in every moment of the interval $[0, T]$. The probability of event $A$ occurring at all in this interval is $p$. Given that $A$ hasn't occurred in the interval $[0,t]$ what's the probability that $A$…
peter.petrov
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Average time waiting for bus

There are two buses: first arrives to the bus top every 8 minutes, and second arrives every 12 minutes. What is the average waiting time on a bus stop if we take whatever came first? It is expected that buses arrive at regular intervals, so first…
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Probability of a sequence of coin tosses ending in $HHT$ (I win) or $THH$(You win)

I'm still learning undergraduate probability. I was asked this probability puzzle in a recent quantitative developer interview. I solved the first part of the question, using brute-force. I think, brute-force very quickly becomes unwieldy for the…
Quasar
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After $10$ inspections with no defect, whats the prob of that number of inspection is no more than $20$?

I have a problem which I'm not sure how to solve. It goes as follows: A production line has a $5$% defective rate, and its products are inspected one by one until the first defect is found. Given that the first $10$ inspections do not find any…
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Probability given in the form of $a^{-x}$. Is my answer correct?

I'm having trouble solving this exercise about probability, as I'm new to the subject. It says: There is a bus supposed to arrive at 8:00. The probability of it to set out with $m$ minutes of delay is $p_m = 3^{-m} (m = 1; 2; 3; ... ;m \neq 0)$. Due…
user577725
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Is probability-raising closed under union?

Suppose that $\Pr(X \mid A) > \Pr(X)$, and that $\Pr(X \mid B) > \Pr(X)$. Does it follow that $\Pr(X \mid A \cup B) > \Pr(X)$? $\Pr(X \mid A \cup B) > \Pr(X)$ holds just in case $$ [\Pr(X A) - \Pr(X) \cdot \Pr(A)] + [\Pr(XB) - \Pr(X) \cdot \Pr(B)]…
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(Paul Bartha and Christopher Hitchcock, “The Shooting Room Paradox and Conditionalizing on Measurably Challenged Sets,” Synthese, March 1999)

I first read this problem here. I am having trouble finding the expected value of the game. I understand for the first round,but on the 2nd round assuming that no group is killed, does just one person role the dices and if not (6,6), then someone…
yiyi
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