Mathematics Stack Exchange
Mathematics Stack Exchange

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
6
votes
3 answers

How many times do we need to roll a fair die to get a better than evens chance of at least one six?

"How many times do we need to roll a fair die to get a better than evens chance of at least one six?" This is the question i need to answer as it is on a practice exam paper. I simply cannot understand how you can increase the chance of getting a 6?…
Bernard.Mathews
  • 61
6
votes
2 answers

Interview Puzzle

Suppose $5$ blue points and $5$ red points are selected in the interval $[0,1]$. What is the probability that the points will interleave each other? Interleave as in one blue point followed by one red point and so on or one red point followed by a…
Kushal Sharma
  • 479
  • 3
  • 8
6
votes
1 answer

Application of Kolmogorov three series theorem in Homework Problem

I have a homework problem which I encounter some difficulty in. I sincerely hope you all can assist me in attempting the following question: Given a sequence of i.i.d random variables $(X_n)_{n \in \mathbb{N}}$ with the condition that…
Novice
  • 719
6
votes
1 answer

How difficult is to find a small clear round spot on a large sheet contaminated by random dirty dots

The problem arose after a discussion why larger digital camera photo sensors is much more expensive than little bit smaller ones, and the reason was given that it's due to difficulty of finding a larger area spot on a big CCD or CMOS panel. Consider…
mbaitoff
  • 853
6
votes
3 answers

Probability a die will come up 6 at least twice in twelve rolls

What is the probability of rolling at least two 6's on twelve rolls of a fair 6-sided die. I am using the complement to solve the question $$1-\frac {5^{12}+(_{12}C_ 1)5^{11}}{6^{12}}$$ $5^{12}$ is the probability of not rolling a six $6^{12}$ is…
John Petryk
  • 151
6
votes
1 answer

Probability: Drawing Aces from a Deck of Cards

"You are dealt 13 cards randomly from a pack of 52. What is the probability your hand contains exactly 2 aces?" I thought about breaking it down into: ${4 \choose 2}$ = number of ways to choose two of four aces. ${48 \choose 11}$ = number of ways to…
Abhishek M.
  • 61
6
votes
1 answer

Union of two events is at least as likely as the product of the events' probabilities

If $A$ and $B$ aren't disjoint and $A \cup B \neq \Omega$, then is $P(A \cup B) \geq P(A)P(B)$? My only idea is to use $P(A \cup B) = P(A) + P(B) - P(A \cap B)$ but there's a minus in front of the intersection and the events don't have to be…
johnsmith
  • 343
6
votes
0 answers

Calculate the speed of the slowest flying machine in Minecraft with probabilities

In Minecraft (sandbox video game made of blocks,written in Java), I have recently created a flying machine (assemble of blocks which moves on its own) and I have trouble calculating its speed, I hope someone can help me. Topic :…
Dryhb
  • 61
  • 2
6
votes
1 answer

Sum of N i.i.d. random variables

Suppose I have a random variable $X_i$ with pdf $$X_i = \begin{cases}1 & P(X_i=1)=p\\-1 & P(X_i=-1)=q\\0 & P(X_i=0)=1-p-q\end{cases}$$ What is the pdf of sum of $N$ such i.i.d. random variables, i.e. $$X = X_1+X_2+\dots+X_N$$
Subhash Lakshminarayana
  • 91
6
votes
1 answer

Expected return value of a recursive probabilistic function

In this question asked on Stackoverflow, the asker gives a Java function similar to this: public int f(){ if(Math.random() >= 0.5){ return 1; } else{ return 1 + Math.max(f(), f()); } } In math-speak, that would be…
BlueRaja - Danny Pflughoeft
  • 8,434
6
votes
1 answer

Probability of partially sortedness of a perfectly shuffled array of unique numbers

Sorry that I don't know any better way to express this question. Assuming that we have a perfectly shuffled array of unique numbers, we know that the array is in fact consisted of ascending or descending sorted subarrays. In average howmany such…
Redu
  • 231
6
votes
6 answers

Probability of 2 Cards being adjacent

I read about a magic trick yesterday that relied on probability - I gave it a try a few times and it seemed to work, but I was wondering what the actual probability of success is. I understand basic probability but I'm not quite sure how I would…
user88450
6
votes
1 answer

Calculating expected value of choosing red ball from 5 bins of different sizes

MY ATTEMPT AT SOLUTION: $P(win)=P(draw.at.least.3. red)=P(draw 3 R)+P(draw 4 R) + P(draw 5 R)$ Using the law of total…
user130306
  • 1,890
6
votes
2 answers

Maximum probability without the Optimal strategy

I've been stuck on this problem for a good 2 days now, I don't feel any closer to solving it. It reads: "Pick a natural number between $0$ and $100$ inclusive; denote this number as $\mathit{n}$. Define a process that terminates at either $0$ or…
PythonCZX
  • 103
6
votes
2 answers

What's the probability of me being obliterated if Thanos snaps his fingers twice?

Thanos snaps his fingers and half the Earth's population disappear. He snaps again and half of the remaining half disappear. Now, what is the probability of any given person (for example, myself) disappearing after 2 snaps? My simplistic reasoning…
Enic
  • 83
1 2 3
…
99 100