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
4
votes
1 answer

Probability of getting exactly 3 red hats or 3 blue hats

A drawer holds $4$ red hats and $4$ blue hats. What is the probability of getting exactly $3$ red hats or $3$ blue hats when taking out $4$ hats randomly out of the drawer and immediately returning every hat to the drawer before taking out…
Mahmudul Hasan
  • 711
4
votes
6 answers

The probability of scoring a 2 just once when a die is thrown three times?

A die is thrown three times. Show the probability of scoring a $2$ on just one occasion in the probability tree diagram and find the probability. My Approach: When a die is thrown once, the sample space is $6$. When it is thrown twice, the sample…
pi-π
  • 7,416
4
votes
1 answer

Computing a certain probability.

Imagine a gun that is shooting a ball in a square of $(0,1) \times (0,1)$ as the figure below, So we can assume that the coordinates $(X,Y)$ are random variables with a uniform distribution on $(0,1)$ so if we let $W$ to be the random variable…
user162343
  • 3,245
4
votes
1 answer

Probability of a person living at least $t$ years

Suppose the force of mortality of a person aged $x$ is $\mu_x = \frac{1}{200-x} + \frac{1}{100-x}$ where $x<100$. What is the probability that the person survives at least $t$ more years? So would this be $$\exp \left(-\int_{x}^{x+t} \frac{1}{200-s}…
studentquestion
  • 63
4
votes
2 answers

What's the probability that space shuttle will fly?

Ques. NASA is developing two top-secret space shuttles. One has two engines, the other has four. All the engines are identical, and have the same probability of failure. Each is designed to fly if at least half of its engines work. A visiting…
User
  • 2,938
4
votes
1 answer

Sequence of events probability proof

So, here's the problem (1.5.12, Probability and Statistics, Degroot and Schervish 3e) : Let $ A_1, A_2, ... $ be an arbitrary infinite sequence of events, and let $ B_1, B_2, ... $ be another infinite sequence of events defined as follows: $B_1 =…
Tyler
  • 2,857
4
votes
1 answer

Understanding Conditional Probability with More than 2 Events

Is there a difference between: $$p(y|x,z) = \frac{p(y,x|z)}{p(x|z)}$$ and $$p(y|x,z) = \frac{p(y,x,z)}{p(x,z)}$$ I was working on a problem that asks one to prove $p(x, y|z) = p(x|z)p(y|x, z)$ and the second one just came to my mind.
John
  • 41
4
votes
3 answers

Probability that the final molecule removed from urn $ 1 $ is red

$ \textbf{Question:} $ (from Ross' $ \textit{A First Course in Probability}) $ Urn $ 1 $ initially has $ n $ red molecules and urn $ 2 $ has $ n $ blue molecules. Molecules are randomly removed from urn $ 1 $ in the following manner: After each…
user298251
4
votes
3 answers

Conditional Probability: Two die randomly chosen with red and blue faces

I have been going through and doing some (non-assessed) homework questions, but am getting really stuck on conditional probability. The following problem is one that I simply cannot get my head around. Question: Die A has four red and two blue…
Guest
  • 79
4
votes
3 answers

Probability that a player wins a card guessing game

$ \textbf{Question:} $ A card game consists of $ n $ cards $ (n \ge 1), $ one of which is a special card. The cards are shuffled randomly and then turned over one at a time. At any time, a player must guess whether the current card is the special…
user298251
4
votes
2 answers

Stopping time problem with random translations on the unit interval

You take a circle centered at the origin, spin it at random, and paint the part in the first quadrant. You repeat the spinning and painting until the circle is completely covered with paint. The problem is just to compute the average number of spins…
Rus May
  • 2,087
4
votes
1 answer

Probability of 20 heads without getting 2 tails in a row, versus 10 heads without getting 1 tail

Are the odds of flipping a coin and getting 20 heads without getting 2 tails in a row the same as flipping a coin and getting 10 heads without getting 1 tail?
Triumph
  • 81
4
votes
3 answers

$x,y,z$ independent and uniform random on $[0,1]$, $P(x \geq yz)$?

$x,y,z$ are independent and uniform random on $[0,1]$. I know that $P(x \geq yz) = 3/4$ by triple integrating the triple density function. However, is there a easier way to get this solution? Without triple integration.
Legendre
  • 2,845
4
votes
2 answers

How does a pity timer affects probabilities?

In a game called hearthstone you buy packs to collect cards. They have four types of cards. Each type of cards has assigned a probability. So you open a pack and a random number is generated. The most valuable cards (called legendary) as you may…
beto
  • 41
4
votes
1 answer

Probability of picking a uniquely colored ball

I came across an interesting problem on probability which is as follows: Consider that there are two buckets A and B. A has N differently numbered balls {1,2,3,...,N} while B has a subset of balls that are already in A. e.g. N = 5, A =…
Mobashyr Mohammad
  • 43
1 2 3
…
99 100