Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [conditional-probability]

For questions on conditional probability.

Conditional probability is the probability that an event occurs given that another event has already happened. The probability of an event $A$ given another event $B$ is written as $P(A|B)$, and is related to the marginal and joint probabilities via $$ P(A|B)P(B)=P(A\cap B)$$

5658 questions
0
votes
0 answers

Bayes Theorem Basic Problem.

Subject in an experiment are told that either a red or a green light will flash. Each subject is to guess which light will flash. The subject is told that the probability of a red light is 0.7, independent of guesses. Assume that the subject is a…
Meghansh Agrawal
  • 1
0
votes
1 answer

If I know $P(x)$ and $P(y|x)$, how can I know $P(y)$?

If I need to compute $P(y)$ and I only know $P(y|x)$ and $P(x)$. I know that: $$P(y|x)=\frac{P(y,x)}{P(x)}$$ This is the contingency table for $P(y|x)$: P(y|x) | +x | ¬x | ------------------------- +y | 0.91 | 0.03…
VansFannel
  • 358
0
votes
3 answers

Bernoulli distribution conditional distribution

Two Independent variables have Bernoulli distribution: $X_1$ with $b(n,p)$ and $X_2$ with $b(m,p)$. How can I find conditional distribution $\mathbb P(X_1|X_1+X_2=t)$?
Azsb
  • 1
  • 3
0
votes
1 answer

Showing conditional independence in a graphical model

In a graphical model, we say that set $A$ and $B$ are conditionally independent given set $C$ if all routes from $A$ to $B$ are blocked. There are multiple ways for the route to be blocked at a node. One instance for the route to be blocked at a…
Sean Lee
  • 1,295
0
votes
1 answer

Conditonal probability question concerning vampires. Genetic variation.

For any individual x born in Transylvania with a vampire father, there is a 50% chance that x is a vampire, independently for each birth. These are the only conditions under which a new vampire can be created. 75% of the Transylvanian males are…
Sam Oh
  • 5
0
votes
1 answer

effect of knowing birthday of one person and the gender on probability of the second gender

Consider there are two applicants for a job. One of the applicants is a man, and it is known that he was born on a Wednesday. What is the probability that the second applicant is also a man? (I am sure its not 1/2)
Olin
  • 5
0
votes
1 answer

Conditional Probability - Red and black marbles

I saw this question on one of the app. A wise man presents you with an urn containing an equal number of red and black marbles. If you reach in and draw two marbles (uniformly and independently) at random from the urn, the probability that they're…
Himanshu Agarwal
  • 19
  • 2
0
votes
1 answer

Condition Probability - 2n+1 trading signals

You are a trader considering a stock whose next price movement will be up or down with equal probability. Fortunately, you have access to a binary signal that is predictive of the price change (and observable ahead of time). The signal is 60%…
Himanshu Agarwal
  • 19
  • 2
0
votes
2 answers

Can events come from different sample spaces in conditional probability?

On $P(B|A)$, can $A,B$ come from different sample spaces? When we talk about the relationship between weather($A$) and stock market($B$), $A$ and $B$ seem to come from totally different sample spaces. But according to the definition of conditional…
William
  • 221
0
votes
1 answer

probability of having specific numbers in an array selected from another array

Let's assume that A = {1,2,3,4,5,6}. 3 numbers are selected from A in a repeated manner. Therefore, there are 6x6x6=216 possibilities which are; …
Talha
  • 1
  • 1
0
votes
0 answers

Two players A and B throw a pair of dice

If two players A and B throw a pair of dice. A will win if he gets a sum of 7 and B will win if he gets a sum of 5. If A starts the game what is the probability that 3 will appear on one of the die in the last throw
J RAVINDRANATH
  • 1
0
votes
2 answers

how to prove Bayes theorem?

how to prove Bayes theorem? (Develop from conditional probability ) 2 criterias -Total of law is probability -multiplication rule Can someone show me the mathematical proof & steps for this please?
Amber
  • 1
0
votes
1 answer

Basic conditional probability problem

I found this problem in the Sheldon Ross book: In a certain community, 36 percent of the families own a dog and 22 percent of the families that own a dog also own a cat. In addition, 30 percent of the families own a cat. What is (a) the probability…
nordrhein
  • 1
0
votes
1 answer

Conditional Probability of multiple independent events.

This problem is from my teacher and I think their answer is wrong. The problem is in the context of trapping rats. I agree with my teacher for the answer in part A as that is just $$P(R=1)=3(0.3\cdot0.7\cdot0.7)=0.441$$ I do not agree with my…
Zavier
  • 43
0
votes
1 answer

could you help me solve this : Conditioning on a household is affected by this virus, what is the probability that this household has a pet?

virus is spreading in a city. 6% of households who have pets will be affected, while 1% of households without pets will be affected. In this city, about 20% of the households have pets and 80% don't. Conditioning on a household is affected by this…
Mohamed Medhat Ali
  • 3
1 2 3
…
15 16