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
8
votes
2 answers

Dice throwing probability of three different faces.

A standard six side die is rolled three times. Find the chance that three different faces appear? My thoughts: Probability p(same face pops up is)= $1- P$. You roll first one and record what you get. The probability of next (2) two rolls give you…
juniorgraduation2013
  • 155
  • 1
  • 2
  • 10
8
votes
3 answers

Let $X$ be the number of aces and $Y$ be the number of spades. Show that $X$, $Y$ are uncorrelated.

A deck of 52 cards is shuffled, and we deal a bridge of 13 cards. Let $X$ be the number of aces and $Y$ be the number of spades. Show that $X$, $Y$ are uncorrelated. Here is what I did: $Cov(X,Y) = E[XY]-E[X]E[Y]$ uncorrelated means $Cov(X,Y) = 0$,…
user59036
  • 1,525
8
votes
7 answers

By means of an example, show that $P(A) + P(B) = 1$ does not mean that $B$ is the complement of $A$

I'm in grade 10, and I've just started to learn about complementary events. I am rather perplexed with this question. Isn't this question kinda contradictory, since $P(A) + P(A') = 1$? This is what I got to: $P(A) + P(B) = 1$ $P(A) + P(A') = 1$ How…
Gordon Ng
  • 89
8
votes
7 answers

The probability of Bus A arriving before Bus B

Bus A arrives at a random time between 2pm and 4pm, and Bus B arrives at a random time between 3pm and 5pm. What are the odds that Bus A arrives before Bus B? My understanding is that since Bus B cannot possibly arrive between 2 and 3, we can only…
IrinaS
  • 95
8
votes
7 answers

We have two red, two white and two green marbles in an urn

We have two red, two white and two green marbles in an urn. We pick them one by one out of the urn and record their colors. Find the probability that at some point we will pick the same color back to back. For example, this happens when we get…
Stackman
  • 4,028
8
votes
2 answers

Exit poll in elections

We want to run an exit poll for the government referendum, by asking the voters in one vote center whether they voted for option A or B. We have an urn with 5 red, 3 green and 2 blue marbles. Each voter randomly picks one marble from the urn,…
Eduardo Juan Ramirez
  • 437
8
votes
1 answer

Binomial distribution and upper bound

This is from Feller's Introduction to Probability Theory and Its Applications. In the context of Bernoulli trials, we define: $$b(k;n,p) = \binom{n}{k}p^kq^{n-k},$$ $$P\{S_n \ge r\} = \sum_{v=0}^{\infty}b(r+v;n,p).$$ The latter being the probability…
user519
8
votes
3 answers

What is the probablity of sitting next to my friend?

Let's say you are at a table with $5$ others, everyone is seated randomly around a $6$ person table, and you only know $1$ person at this party. What is the likelihood you sit next to the individual that you know? What is the likelihood you are…
fsdff
  • 235
8
votes
2 answers

Charged particles

We are creating a circular hub consisting of charged 0 and 1 particles next to each other, beginning with four of them: 0, 1, -0 and -1 in this order. Every 1 sec we randomly select one of each kind and add it next to the last one. Whenever a 0…
Sal.Cognato
  • 1,527
8
votes
2 answers

Product of probability density functions

I was going through a problem in Geoffrey Grimmett and David Stirzaker's book (Probability and Random Processes). The problem is as follows: If $f$ and $g$ are probability density functions, then prove that for $ 0 \leq \lambda \leq 1$ the function…
jay-sun
  • 930
  • 6
  • 13
8
votes
2 answers

when is a longer series BAD for the better team?

This question is inspired by: A longer series is better for a better team: Can you see this at a glance? Also obviously inspired by the NBA playoffs happening right now. :) Suppose two teams are playing a series of $2k-1$ games, and the first team…
antkam
  • 15,363
8
votes
4 answers

What is the probability that both children are boys if at least one is a boy born on a Tuesday?

A family has two children. Given that at least one of the children is a boy who was born on a Tuesday, what is the probability that both children are boys? The day of birth is independent of the gender P(both are boys $\mid $ at least one boy) =…
Busi
  • 572
8
votes
2 answers

Probability question.

Consider a random process where integers are sampled uniformly with replacement from $\{1,\ldots,n\}$. Let $X$ be a random variable that represents the number of samples until a duplicate is found. So if the samples were $1,6,3,2, 5,1$ then $X=6$.…
user54551
8
votes
3 answers

How do I know when to use the Law of total probability?

I am studying Probability Theory 1, and we have learned the Law of total probability and proved it. I know the theoretical intuition behind it and I know why it makes sense from it's proof. But when I see a new problem (that they solved it using…
atefsawaed
  • 961
8
votes
1 answer

Is it possible to find a lower bound of this integral $\displaystyle\int^A_0 (A-x)p(x)\ dx$?

Is it possible to find a lower bound of this integral? $\displaystyle\int^A_0 (A-x)p(x)\ dx$. Here $p(x)$ is some probability distribution with known mean and standard deviation and $A$ is a constant. I was trying to simplify this as…
Dip
  • 125
  • 4
1 2 3
…
99 100