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Welcome to GATE CSE Doubts, where you can ask questions and receive answers from other members of the community.

Recent questions tagged conditional-probability

0 votes
0 answers 56 views
Combinatorics and propositional logic : Probability - 1. https://gateoverflow.in/questions/mathematics/probability 2. https://gatecse.in/probability/ 3. https://gateoverflow.in/tag/random-variable 4. https://gateoverflow.in/tag/random-variable?start=90 5. https:/ ... relations, generating functions - Rosen Chapter 6, 8 ... https://drive.google.com/file/d/0Byt7-j-JD0d0bmxlRkZGcjN2cjA/view
asked Jul 21 in GATE asqwer 633 points 56 views
3 votes
2 answers 670 views
A sender $(\textsf{S})$ transmits a signal, which can be one of the two kinds: $H$ and $L$ with probabilities $0.1$ and $0.9$ respectively, to a receiver $(\textsf{R})$. In the graph below, the weight of edge $(u,v)$ is the probability of receiving $v$ ... $0.7$. If the received signal is $H,$ the probability that the transmitted signal was $H$ (rounded to $2$ decimal places) is __________.
asked Feb 18 in Probability Arjun 1.5k points 670 views
0 votes
1 answer 59 views
Six people, including A,B, and C, form a queue in a random order (all 6! orderings are equiprobable). Consider the event "B is between A and C in the queue". What is its probability? (The order of A and C can be arbitrary, but B should be between them).
asked Aug 5, 2020 in Probability aryashah2k 2 points 59 views
0 votes
2 answers 420 views
Six people including A,B, and C, form a queue in a random order (all 6! orderings are equiprobable). Consider the event "A precedes B in the queue". (Again this event does not mention C or other people in the queue. It happens when A is closer to the start of the ... B, and does not require that B is the next after A, some people could be between A and B.) What is the probability of this event?
asked Aug 5, 2020 in Probability aryashah2k 2 points 420 views
0 votes
1 answer 82 views
1. Most mornings, Victor checks the weather report before deciding whether to carry an umbrella. If the forecast is rain, the probability of actually having rain that day is 80%. On the other hand, if the forecast is no rain, the probability of it actually raining is ... was rain if it was during the winter? What is the probability that the forecast was rain if it was during the summer?
asked Jul 20, 2020 in Probability neeraj_bhatt 475 points 82 views
0 votes
0 answers 13 views
Suppose a fair six-sided die is rolled once. If the value on the die is $1, 2,$ or $3,$ the die is rolled a second time. What is the probability that the sum total of values that turn up is at least $6$ ? $\dfrac{10}{21}$ $\dfrac{5}{12}$ $\dfrac{2}{3}$ $\dfrac{1}{6}$
asked Apr 18, 2020 in Probability admin 573 points 13 views
0 votes
0 answers 19 views
Let $A$ and $B$ be any two arbitrary events, then, which one of the following is TRUE? $P (A \cap B) = P(A)P(B)$ $P (A \cup B) = P(A)+P(B)$ $P (A \mid B) = P(A \cap B)P(B)$ $P (A \cup B) \leq P(A) + P(B)$
asked Apr 18, 2020 in Probability admin 573 points 19 views
0 votes
0 answers 14 views
Consider Guwahati, (G) and Delhi (D) whose temperatures can be classified as high $(H)$, medium $(M)$ and low $(L)$. Let $P(H_G)$ denote the probability that Guwahati has high temperature. Similarly, $P(M_G)$ and $P(L_G)$ denotes the probability of ... , then the probability (correct to two decimal places) that Guwahati has high temperature given that Delhi has high temperature is _____
asked Apr 18, 2020 in Probability admin 573 points 14 views
0 votes
0 answers 10 views
$P$ and $Q$ are considering to apply for a job. The probability that $P$ applies for the job is $\dfrac{1}{4},$ the probability that $P$ applies for the job given that $Q$ applies for the job is $\dfrac{1}{2},$ and the probability that $Q$ applies for the job given that $P$ applies ... $\left(\dfrac{4}{5}\right)$ $\left(\dfrac{5}{6}\right)$ $\left(\dfrac{7}{8}\right)$ $\left(\dfrac{11}{12}\right)$
asked Apr 18, 2020 in Probability admin 573 points 10 views
0 votes
0 answers 18 views
Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than $100$ hours given that it is of Type $1$ is $0.7$, and given that it is of Type $2$ is $0.4$. The probability that an LED bulb chosen uniformly at random lasts more than $100$ hours is _________.
asked Apr 18, 2020 in Probability admin 573 points 18 views
0 votes
0 answers 10 views
Let $P(E)$ denote the probability of the event $E$. Given $P(A) = 1$, $P(B) =\dfrac{1}{2}$, the values of $P(A\mid B)$ and $P(B\mid A)$ respectively are $\left(\dfrac{1}{4}\right),\left(\dfrac{1}{2}\right)$ $\left(\dfrac{1}{2}\right),\left(\dfrac{1}{4}\right)$ $\left(\dfrac{1}{2}\right),{1}$ ${1},\left(\dfrac{1}{2}\right)$
asked Apr 18, 2020 in Probability admin 573 points 10 views
0 votes
0 answers 11 views
$10$% of the population in a town is $\text{HIV}\large ^{+}$. A new diagnostic kit for $\text{HIV}$ detection is available; this kit correctly identifies $\text{HIV}\large ^{+}$ individuals $95$% of the time, and $\text{HIV}\large ^{-}$ ... of the time. A particular patient is tested using this kit and is found to be positive. The probability that the individual is actually positive is ______.
asked Apr 18, 2020 in Numerical Ability admin 573 points 11 views
0 votes
0 answers 7 views
You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is $\dfrac{1}{4}$ $\dfrac{1}{3}$ $\dfrac{1}{2}$ $\dfrac{2}{3}$
asked Apr 18, 2020 in Probability admin 573 points 7 views
0 votes
0 answers 13 views
Box $P$ has $2$ red balls and $3$ blue balls and box $Q$ has $3$ red balls and $1$ blue ball. A ball is selected as follows: (i) select a box (ii) choose a ball from the selected box such that each ball in the box is equally likely to be chosen. The probabilities of selecting boxes ... the probability that it came from the box $P$ is: $\dfrac{4}{19}$ $\dfrac{5}{19}$ $\dfrac{2}{9}$ $\dfrac{19}{30}$
asked Apr 18, 2020 in Probability admin 573 points 13 views
0 votes
0 answers 14 views
A coin is tossed thrice. Let X be the event that head occurs in each of the first two tosses. Let Y be the event that a tail occurs on the third toss. Let Z be the event that two tails occur in three tosses. Based on the above information, which one of the following statements is TRUE? X and Y are not independent Y and Z are dependent Y and Z are independent X and Z are independent
asked Apr 18, 2020 in Numerical Ability admin 573 points 14 views
0 votes
0 answers 37 views
An automobile plant contracted to buy shock absorbers from two suppliers $ X$ and $ Y$ . $ X$ supplies $60\%$ and Y supplies $40\%$ of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of $ X's$ ... a randomly chosen shock absorber, which is found to be reliable, is made by $Y$ is $0.288$ $0.334$ $0.667$ $0.720$
asked Apr 18, 2020 in Numerical Ability admin 573 points 37 views
0 votes
0 answers 7 views
In a factory, two machines $M1$ and $M2$ manufacture $60\%$ and $40\%$ of the autocomponents respectively. Out of the total production, $2\%$ of $M1$ and $3\%$ of $M2$ are found to be defective. If a randomly drawn autocomponent from the combined lot is found defective, what is the probability that it was manufactured by $M2$? $0.35$ $0.45$ $0.5$ $0.4$
asked Apr 18, 2020 in Numerical Ability admin 573 points 7 views
0 votes
0 answers 9 views
The probability of an event $B$ is $P_1$. The probability that events $A$ and $B$ occur together is $P_2$ while the probability that $A$ and $\bar{B}$ occur together is $P_3$. The probability of the event $A$ in terms of $P_1, P_2$ and $P_3$ is _____________
asked Apr 18, 2020 in Probability admin 573 points 9 views
0 votes
1 answer 50 views
The king comes from a family of 2 children. What is the probability that the other child is his sister? A couple has 2 children. What is the probability that both are girls if the older of the two is a girl? my attempt for q-7 Sample space={BG, GB, BB} there must ... be the same then sample space will be {GB, GG}] Ain't both the questions similar? Also please explain where am I going wrong in q-8
asked Jun 30, 2019 in Probability aditi19 53 points 50 views
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