Conditional probability Definition and 242 Threads

Homework Statement A population has n men and n women. If you where to take 4 people out of the population to form a group what's the probability that there are exactly the same number of men as women in the group . Homework Equations The Attempt at a Solution Ok so I thought...

Okay so I have a complex setup that I hope I can convey. I have 9 sites to which X can bind. 6 out of the 9 sites are active and 3 out of the 9 sites are inactive. I need 3 of the active sites to be bound to get the response I am looking for - which we will call EMAX. So when I add a...

What I mean by this is, Say I roll a die, given the specific condition that I get four eights consecutively such as "8888", the same probability as if I give the specific condition that I get another specific non-consecutive number such as? "0248" OR Say I flip a quarter. Would the...

1. Assume that there is a 50% chance of hard drive damage if a power line to which a computer is connected is hit during an electrical storm. There is a 5% chance that an electrical storm will occur on any given summer day in a given area. If there is a 0.1% chance that the line will be hit...

So,I'm studying statistics (for engineers) now,and this is one of them courses that really gives me a headache time after time. Here for example,I can't seem to get the difference between P(A\bigcapB),and P(A|B).I'l give an example in for of a question given to us in some class. "70 percent...

Homework Statement You start out with a bag that contains either a red marble or a green marble with equal probability. Then, a red marble is added to the bag. If I draw out a red marble the first time, what is the probability of drawing out a green marble the second time? Homework...

Hi all, While solving problems related to probability I got stucked with this problem: In some election 4 candidates A,B,C,D has the probability of being elected is 0.4,0.3,0.2,0.1 respectively.If the candidate C discard his candidateship just prior to the election ,then what will be the...

Homework Statement A standard deck of 52 cards of 4 suits, each with 13 denominations, is well shuffled and dealt out to four players, N, S, E and W, who each receive 13 cards. If N and S have exactly ten cards of a specified suit between them, show that the probability that three remaining...

Homework Statement Suppose we have 10 coins such that if the ith coin is flipped, heads will appear with probability i/10, i = 1,2...10. When one of the coins is randomly selected and flipped, what is the conditional probability that it was the coin? Homework Equations Bayes's Formula...

Homework Statement Consider 3 urns. Urn A contains 2 white and 4 red balls, Urn B contains 8 white and 4 red balls and Urn C contains 1 white and 3 red balls. If 1 ball is selected from each urn, what is the probability that the ball chosen from urn A was white given that exactly 2 white...

Homework Statement We are given a belief network such that the overall joint probability after accounting for conditional independence is: P(a,b,c,d,e) = P(a)P(c|a,b)P(d|b)P(e|d,b) The values provided are: P(a = false) = .02 P(b = false) = .95 P(c= false|a=true, b=true) = .97 P(c=...

What I mean by this is, Say I roll a die, given the specific condition that I get four eights consecutively such as "8888", the same probability as if I give the specific condition that I get another specific non-consecutive number such as? "0248" Thanks

Bob picks 3 cats. There are 5 striped males, 6 striped females, 8 spotted males, and 4 spotted females. What is the prob. that Bob has atleast a striped cat given that he has picked at least a female? ------------------------------------------------------ I have: (prob. of a striped...

1. You give a friend a letter to mail. He forgets to mail it with probability 0.2. Given that he mails it, the Post Office delivers it with probability 0.9. Given that the letter was not delivered, what’s the probability that it was not mailed? 2. I assume I'm supposed to use Bayes...

Hi there, I have the journey times of 2 journeys. Would somebody be able to show me by way of example how to calculate the conditional probability function of the second journey time given the first journey time? https://dl.dropbox.com/u/54057365/All/jt.JPG Appreciate your help Thanks John

Homework Statement Of the items produced daily by a factory, 40% come from line I and 60% from line II. Line I has a defect rate of 8%, whereas line II has a defect rate of 10%. If an item is chosen at random from the day’s production, find the probability that it will not be defective...

My probability class has me wondering about pure math questions now. We started with the axioms and are slowly building up the theory. Everything was fine but then a definition of Conditional Probability P[A|B] = \frac{P[AB]}{P[B]} appeared and it's just not sitting right with me. I know that...

P(S1 \cap S2 \cap S3 | r) How do I simplfy the above equation if S2 and S3 are independent of r ?

I have some problems getting conditional probability right... Does this look like it should? Homework Statement Assume that there are bags of tulip bulbs in the basement, ant that they contain 25 bulbs each. yellow bags contain 20 yellow tulips and 5 red tuplips, and red bags contain 15 red...

1. I am going over some past Probability exam papers and cannot solve this question. Any help or advice would be much appreciated! 2. David eats cereal for lunch 60% of days. If he had ice cream for breakfast, then the probability that he eats cereal for lunch is only 0.25. If he didn't...

Homework Statement Given X,Y RV both have normal distribution with: μ_{x}=6,μ_{y}=4,σ_{x}=1,σ_{y}=5,ρ=0.1 a. are X,Y independent? b. find P(X≤5) c. find P(Y≤5|X=5) 2. The attempt at a solutiona. no -> ρ=0.1 -> cov(X,Y)≠0 b. define Z=\frac{X-6}{1} ; Z~N(0,1) so P(X≤5) = P(Z≤-1) = \Phi(-1)...

You are given a random exponential variable X: f(x) = λ exp(-λ x). Suppose that X = Y + Z, where Y is the integral part of X and Z is the fractional part of X: Y = IP(X), Z = FP(X). Which is the following conditional probability: P(Z < z | Y = n) for 0 ≤ z < 1 and n = 0, 1, … ?

Hello, I'm trying to work out a conditional probability. I have hundreds of measurements of two variables (1) Start Time and (2) Journey time. I've created a frequency table. https://dl.dropbox.com/u/54057365/All/forum.JPG How can I work out the Journey time given a start...

Hello, I'm trying to work out a conditional probability. I have hundreds of measurements of two variables (1) Start Time and (2) Journey time. I've created a frequency table. https://dl.dropbox.com/u/54057365/All/forum.JPG How can I work out the Journey time given a start time? P(JT |...

Homework Statement The Attempt at a Solution I have that the joint probability mass function would be \Pi_{i=1}^{k} \frac{\lambda_{i}^{n_{i}}}{n_{i}!} e^{-\lambda_{i}} How would I go about applying the conditional to get the conditional distribution?

Hi all, My question is the following. Let's say I have two probability distributions; f(x|b)\,g(x|c) b and c are discrete events while x is a continuos variable. i.e When the button b is pressed there is some distribution for the amount of rain fall the next day, x. When the button c...

Need help A system contains two components A & B. The system will function so long as either A or B functions. The probability that A functions is 0.95, the probability that B functions is 0.90, & the probability both function is 0.88. What is the probability that the system functions.

T ≡ "two coins tossed 7 times by two people A and B giving outcomes [A^+B^+, A^-B^+, A^+B^-, A^-B^+, A^+B^+, A^-B^-, A^-B^+], where + = heads and - = tails" Calculate P(A^+B^+|T), P(A^+|T), P(B^+|T) and P(B^+|T,A^+) I asked this question elsewhere and there was a suggestion that the question...

Homework Statement The Attempt at a Solution a) P(Pickwick has no umbrella | it rains) = \frac{\frac{1}{3}\frac{1}{3}}{\frac{1}{2}} = \frac{2}{9}, which is the answer according to my answer key. b) For part b we have: There is a rain forecast which means he will bring the...

Homework Statement Compute P(X=k l X+Y=p)Homework Equations The Attempt at a Solution No idea. Kind of understand page #1. Although it seems like there's a lot of unnecessary stuff. Could have gone straight from the top to the bottom. And I don't know why/if you even have to substitute the...

Homework Statement I've spent a few hours but unable to work out the solution of the following questions successfully. The question is as follows: I am having problems with (a)(iii) and (b)(ii) Homework Equations The Attempt at a Solution (a)(iii) Although I can work...

Guys my question should be easy but I cannot understand how it works, here is how it goes. A murder case involves the death of a guest at a large party in a country house. The police are certain that there is only one murderer who is among the N = 100 remaining people in the house. However...

I have seen in class the following formula used: P(A | C) = \sum_{B} P(A | B \cap C)*P(B | C) I don't understand how this formula works? Can anyone help me understand how it can be derived and how I can understand it intuitively? Can a venn diagram be drawn to illustrate this formula?

Homework Statement I have access to P(x|A) and P(y|A), P(x), P(y) and P(A), in addition to the knowledge that x and y are independent variables. I am interested in finding P(A|x,y). The Attempt at a Solution I think that P(A|x,y) = P(x,y|A) * P(A) / P(x,y) = P(x,y|A) * P(A) /...

Homework Statement A submarine has three navigational devices but can remain at sea if at least two are working. Suppose that the failure times are exponential with means 1 year, 1.5 years, and 3 years. What is the average length of time the boat can remain at sea?Homework Equations Density...

Conditional probability & "r balls randomly distributed in n cells" Homework Statement I'm posting this in hope that someone can give me a correct interpretation of the following problem (problem V.8 of Feller's Introduction to probability theory and its applications VOL I): 8. Seven balls...

Homework Statement A box contains 4 red balls and 6 white balls. A sample size of 3 is drawn without replacement from the box. What is the probability of obtaining 1 red ball and 2 white balls given that at least 2 of the balls in the sample are white? Homework Equations The...

Homework Statement This is a problem I found on web but with no solutions. n Exercise 11 from "Problems on Minterm Analysis," we have the following data: A survey of a represenative group of students yields the following information: 52 percent are male 85 percent live on campus 78...

Say I want to find Pr(A|B). Usually I would just use bayes rule, but some textbooks just assume that A|B works and then just multiply it by P(B). For example in my book, Pr(X>2000)=.4. X and Y are unif distributed from 1000 to 5000. They are independent. Find Pr(X+Y>8000|X>2000). Well they just...

Homework Statement This is in fact an example with solutions. but I don't understand the solutions. So I am here to ask for explanation. Details are; In a city there are equal number of gentleman and ladies. 10% of gentleman are regarded as "good-looking" while 10% of ladies regarded as...

Homework Statement 45% of emails sent to my account is spam. i set up a filter but it fails toquarantine 2% of spam and in advertently quarantines5% of genuine emails. What is the probability that an email will be quarantined as spam? if an email is qurantined as spam what is the...

I was able to do the first part of this problem but unsure how to approach this: Mendel, revisited: Mendel’s peas had either purple or white flowers; flower color is due to a single gene, for which the purple allele (A) is dominant to the white allele (a). We cross two pure-breeding lines...

Homework Statement A manufacturer of scientific workstations produces its new model at sites A, B, and C; 20% at A, 35% at B, and the remaining 45% at C. The probability of shipping a defective model is 0.01 if shipped from site A, 0.06 if from site B, and 0.03 if from site C. A- What is...

Homework Statement Two computers are connected to a password-protected wireless network. When the password is temporarily removed, a virus can attack the first computer with probability 0.5, the second computer with probability 0.7, and it can attack both computers with probability 0.4. The...

Homework Statement I've attached both the problems into one image to make life easier since problem 1 has a diagram and the other does not. Homework Equations Bayes Theorem : P(A|B)P(B) / [P(A|B)P(B) + P(A|B')P(B')] B' = B Complement The Attempt at a Solution well for the first one i don't...

Homework Statement You have 3 urns: Urn 1 has 3 red balls, Urn 2 has 2 red balls, 1 blue ball. Urn 3 has 2 red balls 2 blue balls. You pick a ball from each urn and place it into Urn 4. You draw 2 balls from Urn 4 and they are red. What is the conditional probability that the 3rd ball is also...

A number is selected randomly from a container containing all the integers from 10 to 50 find a) p(even|greater than 40) b) p(greater than 40| even) c) p(prime| between 20 and 40) please provide an explanation, thanks a lot =D

Please, help me to solve the problem Details at a factory are tested randomly to check if they are faulty. It is known from previous experience that the probability of a faulty detail is known to be 0.03. If a faulty detail is tested the probability of it testing faulty is 0.82. If a non-faulty...

Hey guys, first of all I want to say hey to all! I have been a long time lurker and follower of these forums and have been known to find a lot of your answers helping me out throughout my college life. I also know that you just don't like to spit out the answers for those who don't put in...

Two coins are flipped and the results are recorded. Given that one coin lands on a head, find the probability of: a) Two heads, b) a head and a tail Searching online is giving my answers which are not using conditional probability at all, and our teacher told us we have to use the...