Conditional probability Definition and 242 Threads

Conditional Probability... My handout says this... P(m) = .4 P(w) = .5 P(m|w) = .7 Find: P(MnW) = ? P(w|m) = ? P(m or w) = ? P(MnW) = .4 x .5 = .2 P(w|m) = .35/.4 = .875 P(m or w) = ?

If a hand of 5 cards are dealt from a 52 card pack (order doesn't matter), what is the probability that the hand will contain the ace of spades GIVEN that there is at least one ace? Thanks.

Homework Statement A particular brand of cars, say ABC, comes in only two colours, white and grey. Exactly 90% of ABC cars in a particular town are white and 10% are grey. Mrs Z, a witness to a bank robbery, claims to have seen the thieves escaping in an ABC grey car, which taking into...

Homework Statement Given f(x) = e^-x and f(y|x) = 1/x e^(-y/x). Three parts: (a) Compute density of (x,y), (b) Compute E(y) and (c) Compute P(y>x). Homework Equations f(x,y) = f(y|x)f(x) if f(x) = ve^(-vx), then E(x)=v^(-1) The Attempt at a Solution I'm stuck on a problem. I was...

I'm stuck on a problem. I was given f(x) and f(y|x) and was able to derive f(x,y). The second step of the problem is computing P[y>x]. I think I need to know f(y) to answer this problem but I can't figure out how to derive it. Or is there a way to compute P(y>x) given the info I know without...

I'm having trouble with one of the rules of probability P(A n B) = P(A)P(B) which holds if events A and B are independent The following problem illustrates my confusion. I've defined Events A and B below, are these events dependent? Per the solution in the book P(A \cap B) = P(A)P(B)...

There are 15 tennis balls in a box, of which 9 have NOT previously been used. Three of the balls are randomly chose, played with, and then RETURNED TO THE BOX. Later, another 3 balls are randomly chosen from the box. Find the probability that none of these balls has ever been used. Seems...

Homework Statement a family consisting of a father, mother, and a child is chosen at random and is asked on what day of the week each of them was born. What is the probability that all three were born on different days given that the father was born on a monday? Solution: A is the even all...

Homework Statement Suppose a person's score X on a math aptitude test is a number between 0 and 1, and their score Y on a music aptitude test is also between 0 and 1. Suppose further that in the population of all college students in Canada, the scores X and Y are distributed according to the...

Please help me with this. Any suggestions are greatly appreciated. Imagine that I have a bank account. X is the amount of cash on the account at time t+1. Y is the amount of cash at time t. The amount of cash depends on the deposits made and on the amount of cash during the previous period...

This is probably relatively easy, but I'm still a bit confused... The question: A family has j children with probability p1 = .1, p2 = .25, p3 = .35, p4 = .3. A child is randomly chosen. Given this child is the eldest in the family, find the conditional probability that a) Family has 1...

Hello, This question relates to Bayes law. I think my problem is I am not sure of the name of the thing I am trying to derive... I have 2 variables a and b. a = 1 or 0, b = 0...n I have the data to calculate; p(a = 1 and b) p(b) for any b. Hence I can find p(a=1|b) = p(a = 1 and...

hi all, I have a question that i really want to know the answer. the probability that an airplane will return in 10min is 30%, in 20min is 30%, in 30min is 0%, in 40min is 40% according to the past history records. given that the airplane has not return in 20min, what is the probability...

Hi, I am a quantum physicist who needs a practical help from mathematicians. :smile: The physical problem that I have can be reduced to the following mathematical problem: Assume that we have two correlated variables a and b. Assume that we know all conditional probabilities P(a|b), P(b|a)...

Dear all, Please clarify the following: 1.) The difference of conditional probability and Bayes' formula. 2.) Is Bayes' formula a "all weather condition" formula for all conditional probabilities problem? Thank you, S

Dear all, P (A |B) + P (A c|B) = 1 [A c] denotes complement of set A and of course P (B)>0 Is the above statement true? How about the following two: P (A |B) + P (A |B c) = 1 P (C ∪ D|B) = P (C |B) + P (D|B) − P (C ∩ D|B)

Homework Statement In a shipment of 100 televisions, 6 are defective. If a person buys two televisions from that shipment, what is the probability that both are defective? Homework Equations the Answer is somewhat weird! it says it is 1/330 ! which is really beyond by recognition...

Suppose X1 Y1 Z1 0 0 0 (5 times Z1 is 0 for X1=0 and Y1=0) 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 . . . Which is.. (Same table which is above..) X1 Y1 Z1 (Count of Zeros) (Count of...

Hi, I'm trying to work out a probability value from a number of distributions (tests), it gets a little complicated because some of the tests are dependent on each other. Lets say I have a surface which has black and white regions distributed over it, where black is "true" and white is "false"...

I'm trying to solve a problem as part of my research and it's giving me fits. It seems like it should be simple, but I can't wrap my brain around how to do it. The problem is: Suppose X~N(0,s), and Y is a random variable that has a probability mass point at 0 but is otherwise uniformally...

Although this problem may look like homework, I assure you it is not. It is a question that arose from a trading card game that I am stuck on. The problem is as follows (with simplified cards) You have a deck of 53 cards, and 11 of those cards are red and 42 are black. If you were to randomly...

In an election, candidate A receives n votes and candidate B receives m votes, where n>m. Assume that in the count of the votes all possible orderings of the n+m votes are equally likely. Let Pn,m denote the probability that from the first vote on A is always in the lead. Find Pn,m...

[Problem] Stores A, B, and C have 50, 75, and 100 employees, respectively, 50, 60, and 70 percent of these are women. Resignations are equally likely among all employees, regardless of sex. One employee resigns and this is a woman. What is the prob. she works in store C? [Solution] Store A...

conditional probability help please Homework Statement Hi there, I am doing s1 for this jan and i am finding it very difficult to cope up. Especially for probability. I have a cgp buk but stil its not very gud at probability. Here is a question from my text buk which i cud not understand : -...

Homework Statement The probability of a monitor not working is 0.005, the probability of a cpu faulty is 0.002, the probability of a keyboard damaged is 0.0025, what is the probability of the computer switching on? If you are then told that the conditional probability of the monitor not...

Homework Statement Assuming a comp is switched on, the probability that the monitor is not working is 0.005, the probability that the CPU is faulty is 0.02, and the probability that the keyboard cable has been damaged is 0.0025, and that there are no other faults. Proceed to evaluate the...

I say urgent because of the horribly small lecture I received on this section, a whole 3 minutes or so of examples. While I won't give further context I can say without a doubt I am completely lost. Here is the problem I am stuck on. In a string of 12 Christmas tree light bulbs, 3 are...

hi I got a stats problem infornt of me. I figured out that it is abaut conditional probability. But I am stuck :confused: . # hurricanes 0 1 2 3 4 5 6 probability .25 .33 .24 .11 .04 .02 .01 prob >6 is 0 questions are independent. a.)...

At school we have begun conditional probability. Of course, using the conditional probability formula to answer questions is no problem; but i do not fully understand how the formula works. The formula is; Pr(A given or │ B)= Pr(A intersection B)/Pr(B) The the proof for it is self evident...

Hi Everyone, Let's see if someone here can do a better job than my teacher! I have one of the least helpful stat teachers ever. She told me that I was wrong about the following problem. I am not saying that she is wrong or right, but when I asked her to explain why I was wrong, she told me...

Given: P(A)= .4, P(B)=.3, P(A n B)=.11, P(C| not A)=.5 If P(C U A) = .66, then find P[(C U A) | (C n A)]. I have been trying to manipulate this thing for a while now with no luck. Could you try and show the work if not that's alright, I'll work it out. Thanks.

I have to admit I'm struck odd by the this definition: P(A|B) = P(AnB)/P(B) I know conditional probability is the "chance of event a dependant even B happening, given A happens". But really, I don't quite get it... what is meant?

if X and Y are events which are independent of each other, but neither are independent with A, is this equality true for conditional probabilities: P( X, Y | A) = P(X|A) * P(Y|A) if not, how do you solve for P(A | X,Y) given that you only know P (A) and P(X|A) and P(Y|A)? The reason I came...

Please help me to solve the following questions : 1) There are three box : box X has 10 bulbs which 4 are defective Box Y has 6 bulbs which 1 are defective Box Z has 8 bulbs which 3 are defective a box is chosen at random...

An insurance company runs three offices, A, B and C. The company's employess are distirbuted as follows; 30% work in office A, 20% in Off. B and 50% in Off. C. In office A 10% are managers, in office B 20% are managers and in office C 5% are managers a. What is the total proportion of...

Somebody could help me to find out the answer of the interesting question about conditional probability ? "You are moving to other apartment and you need to find your probability book. It is inside of one box. There are n boxes to all. The probability of the book is inside of the box i is Pi...

Q. A box contains three blue marbles, five red marbles, and four white marbles. If one marble is drawn at random, find: a) P(blue|not white) b) P(not red|not white) The answer for both a) and b) is 3/8. However right now I don't even understand the question. part a) wants possibility of...

Hey guys Me and my friend just got this question and it seems easy but i just want to make sure we are right anyway here it is: A road has two stoplights at consecutive intersections. The prob. of a red at the first is 0.55 and the probability of a green at the second, give a green at light...

Question about conditional probability. Can someone help me ? Repulsion. The event A is said to be repelled by the event B is P(A|B) < P(A), and to be attracted by B P(A|B) > P(A). (a) Show that if B attracts A, then A attracts B, and ~B repels A. (b) If A attracts B, and B attarcts C...

Can someone help me with this question ? A random number N of dice is thrown. Let Ai be the event that N = i, and assume that P(Ai) = 1/(2)^i, i >= 1. The sum of the scores is S. Find the probability that: (a) S = 4, given N is even; (b) the largest number shown by any die is r, where S...

Ok guys, I don't really understand conditional probability, can you guys tell me how to go about solving this? To please customers, repairs need to be done satisfactorily and completed on time. For one mechanic, if the job is done on time, he has a 85% chance that it was also done...

In a class of 15 students, 10 are expected to pass maths and 12 are expected to pass english. how many students are expected to pass maths and english? ----- the answer given in the book is 7. i don't understand how this answer was reached. could someone please show me how to calculate...