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https://gateoverflow.in/questions/mathematics/probability
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<p> GATE2008 QUESTION......ans is given c option but the value of probability that we get on putting random valus of r is -ve......then how can c option be the answer........GUYS PLZZ HELP......<img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=1255963995518535773">b</p>Probabilityhttps://gateoverflow.in/169925/gate-previous-yearTue, 14 Nov 2017 05:40:53 +0000#PROBABILITY
https://gateoverflow.in/169628/%23probability
Is there any relation between independent events and mutually exclusive events?Probabilityhttps://gateoverflow.in/169628/%23probabilityMon, 13 Nov 2017 10:08:47 +0000Normal Distribution
https://gateoverflow.in/169307/normal-distribution
Can any one say how to solve Z score questions like below<br />
<br />
1) P(1≤Z≤30) = ?<br />
<br />
2) P(z>2.5)=?<br />
<br />
3) P(z<=k) = 0.9 find k?<br />
<br />
Will they give any related values of Z-scores in exam ?Probabilityhttps://gateoverflow.in/169307/normal-distributionSun, 12 Nov 2017 14:11:09 +0000probability
https://gateoverflow.in/168943/probability
Consider a coin with probability P to be heads. What is the probability that the first head will appear on the even numbered tosses?<br />
<br />
(A) (1 - P) / 2<br />
(B) (1 - P) / (2 - P)<br />
(C) (1 - P) / (3 - P)<br />
(D) 1 / (P (1 - P))Probabilityhttps://gateoverflow.in/168943/probabilitySat, 11 Nov 2017 17:45:25 +0000Finding minima of function.
https://gateoverflow.in/168862/finding-minima-of-function
<p>For what value of 'k' (in terms of $X_{i}$'s) following functions will attain their minimum value $\rightarrow$ </p>
<ol>
<li>$F_{1}(k)$ = $\sum_{i=0}^{n} \left | X_{i} - k \right |$</li>
<li>$F_{2}(k)$ = $\sum_{i=0}^{n}\left ( X_{i} - k \right )^{2}$</li>
</ol>
<p>
<br>
If possible, please provide some valid proof for supporting your answer ?</p>Probabilityhttps://gateoverflow.in/168862/finding-minima-of-functionSat, 11 Nov 2017 15:02:05 +0000Range of covariance and correlation coefficient
https://gateoverflow.in/168800/range-of-covariance-and-correlation-coefficient
Hi Guys,<br />
<br />
How can we prove following $\rightarrow$<br />
<br />
$-\infty \leq Covariance(X,Y) \leq +\infty$<br />
<br />
and <br />
<br />
$ -1 \leq correlationCoefficient(X,Y) \leq +1$Probabilityhttps://gateoverflow.in/168800/range-of-covariance-and-correlation-coefficientSat, 11 Nov 2017 12:31:11 +0000A First Course in Probability- Sheldon Ross 8th Edition Random Variables Example 1b
https://gateoverflow.in/168323/course-probability-sheldon-edition-random-variables-example
Three balls are to be randomly selected without replacement from an urn containing<br />
20 balls numbered 1 through 20. If we bet that at least one of the balls that are<br />
drawn has a number as large as or larger than 17, what is the probability that we<br />
win the bet?Probabilityhttps://gateoverflow.in/168323/course-probability-sheldon-edition-random-variables-exampleFri, 10 Nov 2017 10:04:00 +0000Probability Distribution
https://gateoverflow.in/166925/probability-distribution
Can Anyone who do have some good reference or good material to practice Distribution in probability share the source or material: Specifically :<br />
POISSON and Normal distribution.Probabilityhttps://gateoverflow.in/166925/probability-distributionMon, 06 Nov 2017 15:45:50 +0000PROBABILITY
https://gateoverflow.in/166680/probability
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=6253675655264571246"></p>Probabilityhttps://gateoverflow.in/166680/probabilityMon, 06 Nov 2017 06:37:52 +0000Gate 2012 CE Probability
https://gateoverflow.in/164724/gate-2012-ce-probability
<p><a rel="nofollow" href="https://gateoverflow.in/?qa=blob&qa_blobid=10296109511847257457" target="_self">https://gateoverflow.in/?qa=blob&qa_blobid=10296109511847257457</a></p>Probabilityhttps://gateoverflow.in/164724/gate-2012-ce-probabilityWed, 01 Nov 2017 09:02:06 +0000Probability
https://gateoverflow.in/164529/probability
Suppose two dies are rolled .What is the probability of getting 4 on the first die , when the the sum is 6 ?<br />
<br />
A) 1/5 B)1/6Probabilityhttps://gateoverflow.in/164529/probabilityTue, 31 Oct 2017 16:09:51 +0000Probability
https://gateoverflow.in/162709/probability
<p style="text-align:center"><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=4455391736370149267"></p>
<p> </p>Probabilityhttps://gateoverflow.in/162709/probabilityWed, 25 Oct 2017 14:09:42 +0000Median
https://gateoverflow.in/162030/median
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=16108385487096326986"></p>
<p> </p>Probabilityhttps://gateoverflow.in/162030/medianSun, 22 Oct 2017 16:04:12 +0000GATE 2012
https://gateoverflow.in/161893/gate-2012
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=16029912539662025372"></p>Probabilityhttps://gateoverflow.in/161893/gate-2012Sun, 22 Oct 2017 03:50:56 +0000Gate_branch_question
https://gateoverflow.in/161856/gate_branch_question
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=3985791191016108054"></p>
<p> </p>Probabilityhttps://gateoverflow.in/161856/gate_branch_questionSat, 21 Oct 2017 16:11:50 +0000Gate_other_branch_question
https://gateoverflow.in/161854/gate_other_branch_question
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=3443364138293146065"></p>Probabilityhttps://gateoverflow.in/161854/gate_other_branch_questionSat, 21 Oct 2017 16:09:23 +0000K. Rosen: Probability
https://gateoverflow.in/161474/k-rosen-probability
<p><strong>Why is it 7 in the denominator?</strong></p>
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=683451685459367689"></p>Probabilityhttps://gateoverflow.in/161474/k-rosen-probabilityFri, 20 Oct 2017 04:02:05 +0000probability
https://gateoverflow.in/161146/probability
5 cards are drawn successively with replacement from well shuffled deck of 52 cards.<br />
What is the probability that<br />
i) all the five cards are spades<br />
ii) only 3 cards are spades<br />
iii) none is a spade.Probabilityhttps://gateoverflow.in/161146/probabilityWed, 18 Oct 2017 16:53:25 +0000Gate_other_branch_question
https://gateoverflow.in/160738/gate_other_branch_question
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=17402107356947374621"></p>Probabilityhttps://gateoverflow.in/160738/gate_other_branch_questionTue, 17 Oct 2017 09:17:59 +0000Rossen: Permutation and Combination
https://gateoverflow.in/159455/rossen-permutation-and-combination
What is the probability of these events when we randomly select a permutation of {1, 2, . . . , n} where n ≥ 4?<br />
<br />
a) n precedes 1 and n −1 precedes 2.<br />
b) n precedes 1 and n precedes 2.Probabilityhttps://gateoverflow.in/159455/rossen-permutation-and-combinationThu, 12 Oct 2017 10:57:59 +0000PROBABILITY
https://gateoverflow.in/157774/probability
A box containing 4 red balls and 6 black balls . Three balls are selected randomly from the box one after the another, without replacement . The probality that the selected set has one red ball and two black balls is .<br />
<br />
I am getting this (4/10)*(6/9)*(5/8) is it correct And is order have any significance here.?Probabilityhttps://gateoverflow.in/157774/probabilityFri, 06 Oct 2017 06:39:17 +0000BINOMIAL DISTRIBUTION
https://gateoverflow.in/157752/binomial-distribution
Consider an unbiased cubic dice with opposite faces coloured identically and each face coloured red, blue or green such that each colour appears only two times on the dice. If the dice is thrown thrice, the probability of obtaining red colour on top face of the dice at least twice is----<br />
<br />
I am getting 0.75 can anyone confirm this ?Probabilityhttps://gateoverflow.in/157752/binomial-distributionFri, 06 Oct 2017 05:33:23 +0000test series
https://gateoverflow.in/157656/test-series
A fidget spinner has 3 wings. Each wing is numbered 1, 2,3. After spinning it vertically, the wing which is relatively upper than remaining is chosen. If two fidget spinners are spinned, the sum ‘r’ of the numbers turned up is considered. <br />
Choose the correct statements<br />
<br />
a)Probability (r≥4) = probability(r≤4)<br />
<br />
b)Probability (r≥4) = probability(r≤3)<br />
<br />
c)The probability(r>5) is greater than probability (r=4)<br />
<br />
d)All are falseProbabilityhttps://gateoverflow.in/157656/test-seriesThu, 05 Oct 2017 18:54:43 +0000Sheldon Ross chapter 4 Random variables Qno-72
https://gateoverflow.in/156385/sheldon-ross-chapter-4-random-variables-qno-72
Two athletic teams play a series of games; the first team to win 4 games is declared the overall winner .Suppose that one of the team is stronger than the other and wins each game with prob 0.6,independently of the outcomes of other games.Find the prob for i=4,5,6,7,,,that the sronger team wins the series in exactly i games.Compare the prob that the stronger team wins with the prob that it would win a 2-out-3 series.Probabilityhttps://gateoverflow.in/156385/sheldon-ross-chapter-4-random-variables-qno-72Sat, 30 Sep 2017 15:46:57 +0000Probability
https://gateoverflow.in/155820/probability
Imagine you are given a bag of n balls. You are told that at least 10% of the balls are blue, and no more than 90% of the balls are red. Asymptotically (for large n) how many balls do you have to draw from the bag to see a blue ball with probability at least 2/3? (You can assume that the balls are drawn with replacement.)Probabilityhttps://gateoverflow.in/155820/probabilityThu, 28 Sep 2017 10:29:26 +0000Probability
https://gateoverflow.in/155533/probability
A train and a bus arrive at random between 9 am and 10 am. The train stops for 10 minutes whereas the bus stops for 'x' minutes. Find 'x' such that the probability that the bus and train meet is 0.5.<br />
<br />
How to approach such type of questions ?Probabilityhttps://gateoverflow.in/155533/probabilityWed, 27 Sep 2017 06:05:08 +0000Doubt
https://gateoverflow.in/155166/doubt
<p><strong>A bag contains 10 red marbles, 10 white marbles, and 10 blue marbles. What is the minimum no. of marbles you have to choose randomly from the bag to ensure that we get 4 marbles of same color?</strong></p>Probabilityhttps://gateoverflow.in/155166/doubtTue, 26 Sep 2017 02:49:37 +0000Probability
https://gateoverflow.in/155136/probability
Let X and Y be independent random variables each taking the values -1 or 1 with probability 1/2. Let Z=XY . Show that X,Y,Z are pairwise independent .<br />
<br />
Are they indepenedent ?Probabilityhttps://gateoverflow.in/155136/probabilityMon, 25 Sep 2017 18:30:19 +0000sheldon ross
https://gateoverflow.in/154985/sheldon-ross
Consider the following technique for shuffling a<br />
deck of n cards: For any initial ordering of the<br />
cards, go through the deck one card at a time and<br />
at each card, flip a fair coin. If the coin comes<br />
up heads, then leave the card where it is; if the<br />
coin comes up tails, then move that card to the<br />
end of the deck. After the coin has been flipped n<br />
times, say that one round has been completed. For<br />
instance, if n = 4 and the initial ordering is 1, 2, 3,<br />
4, then if the successive flips result in the outcome<br />
h, t, t, h, then the ordering at the end of the round<br />
is 1, 4, 2, 3. Assuming that all possible outcomes of<br />
the sequence of n coin flips are equally likely, what<br />
is the probability that the ordering after one round<br />
is the same as the initial ordering?Probabilityhttps://gateoverflow.in/154985/sheldon-rossMon, 25 Sep 2017 07:06:06 +0000Sheldon Ross chapter#3 Qno-45
https://gateoverflow.in/153765/sheldon-ross-chapter%233-qno-45
<p>A set of k coupons, each of which is independently a type j coupon with probability
<br>
p<sub>j</sub><sub> </sub>, from j=1 to n ∑ p<sub>j </sub>= 1, is collected. Find the probability that the set contains either
<br>
a type i or a type j coupon.</p>Probabilityhttps://gateoverflow.in/153765/sheldon-ross-chapter%233-qno-45Wed, 20 Sep 2017 17:38:27 +0000Sheldon ross chapter#3 Qno -30
https://gateoverflow.in/153419/sheldon-ross-chapter%233-qno-30
Two balls, each equally likely to be colored either red or blue, are put in an urn.<br />
At each stage one of the balls is randomly chosen, its color is noted, and it is<br />
then returned to the urn. If the first two balls chosen are colored red, what is the<br />
probability that<br />
(a) both balls in the urn are colored red;<br />
(b) the next ball chosen will be red?Probabilityhttps://gateoverflow.in/153419/sheldon-ross-chapter%233-qno-30Tue, 19 Sep 2017 11:01:23 +0000sheldon M ross 4 ed - chapter-3 qno- 25
https://gateoverflow.in/153134/sheldon-m-ross-4-ed-chapter-3-qno-25
Fifty-two percent of the students at a certain college are females. Five percent<br />
of the students in this college are majoring in computer science. Two percent of<br />
the students are women majoring in computer science. If a student is selected at<br />
random, find the conditional probability that<br />
(a) this student is female, given that the student is majoring in computer science;<br />
(b) this student is majoring in computer science, given that the student is<br />
female.<br />
<br />
How to solve this qn by growing tree method?Probabilityhttps://gateoverflow.in/153134/sheldon-m-ross-4-ed-chapter-3-qno-25Mon, 18 Sep 2017 09:01:47 +0000MA 2017
https://gateoverflow.in/152981/ma-2017
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=4719585218381730416"></p>Probabilityhttps://gateoverflow.in/152981/ma-2017Sun, 17 Sep 2017 16:48:27 +0000MA 2013
https://gateoverflow.in/152979/ma-2013
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=11554834656157963260"></p>Probabilityhttps://gateoverflow.in/152979/ma-2013Sun, 17 Sep 2017 16:44:37 +0000MA 2013 MA
https://gateoverflow.in/152978/ma-2013-ma
Let X be an arbitrary random variable that takes values in {0,1,…,10}. The minimum and maximum possible values of the variance of X are<br />
<br />
(A) 0 and 30<br />
<br />
(B) 1 and 30<br />
<br />
(C) 0 and 25<br />
<br />
(D) 1 and 25<br />
<br />
GIVEN ANSWER IS CProbabilityhttps://gateoverflow.in/152978/ma-2013-maSun, 17 Sep 2017 16:42:44 +0000MA 2014
https://gateoverflow.in/152977/ma-2014
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=173441506922385334"></p>Probabilityhttps://gateoverflow.in/152977/ma-2014Sun, 17 Sep 2017 16:41:46 +0000MA 2014
https://gateoverflow.in/152976/ma-2014
The time to failure, in months, of light bulbs manufactured at two plants A and B obey the exponential distribution with means 6 and 2 months respectively. Plant B produces four times as many bulbs as plant A does. Bulbs from these plants are indistinguishable. They are mixed and sold together. Given that a bulb purchased at random is working after 12 months, the probability that it was manufactured at plant A is _____<br />
<br />
GIVEN ANSWER: 0.92 to 0.94Probabilityhttps://gateoverflow.in/152976/ma-2014Sun, 17 Sep 2017 16:40:39 +0000Probability doubt
https://gateoverflow.in/152779/probability-doubt
Three numbers are chosen at random without replacement from {1,2,3,.....,8}. What is the probability that minimum is 3 given that their maximum is 6?Probabilityhttps://gateoverflow.in/152779/probability-doubtSun, 17 Sep 2017 02:50:02 +0000Probability doubt
https://gateoverflow.in/152641/probability-doubt
A box contains 3 coins: two regular coins and one fake two headed P(H )= 1 .you pick up one at random and toss it and gets heads.the probability that it is a two headed coin is....Probabilityhttps://gateoverflow.in/152641/probability-doubtSat, 16 Sep 2017 11:54:26 +0000GATE 2012 MA
https://gateoverflow.in/152551/gate-2012-ma
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=2887404449711765735"></p>
<p>ANSWER GIVEN 0.73-0.77</p>Probabilityhttps://gateoverflow.in/152551/gate-2012-maSat, 16 Sep 2017 06:31:05 +0000GATE 2017 MA
https://gateoverflow.in/152549/gate-2017-ma
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=9673049504830691856"></p>
<p>ANSWER GIVEN IS 0.27-0.37</p>Probabilityhttps://gateoverflow.in/152549/gate-2017-maSat, 16 Sep 2017 06:28:47 +0000GATE 2017 MA
https://gateoverflow.in/152545/gate-2017-ma
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=7133725661348086680"></p>
<p>ANSWER GIVEN IS 4</p>Probabilityhttps://gateoverflow.in/152545/gate-2017-maSat, 16 Sep 2017 06:25:02 +0000GATE 2017 MA
https://gateoverflow.in/152544/gate-2017-ma
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=6913064227682912036"></p>
<p>Answer given is D</p>Probabilityhttps://gateoverflow.in/152544/gate-2017-maSat, 16 Sep 2017 06:22:07 +0000GATE 2015 MA
https://gateoverflow.in/152542/gate-2015-ma
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=6891829485658445850"></p>Probabilityhttps://gateoverflow.in/152542/gate-2015-maSat, 16 Sep 2017 06:18:02 +0000probability
https://gateoverflow.in/152420/probability
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=7189816802564820416"></p>Probabilityhttps://gateoverflow.in/152420/probabilityFri, 15 Sep 2017 15:59:31 +0000GATE 2015 MA
https://gateoverflow.in/152364/gate-2015-ma
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=10236012100461470116"></p>Probabilityhttps://gateoverflow.in/152364/gate-2015-maFri, 15 Sep 2017 10:50:06 +0000GATE 2016 MA
https://gateoverflow.in/152362/gate-2016-ma
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=10576038349030577104"></p>
<p>THE GIVEN ANSWER KEY IS 0.65 to 0.71 I AM GETTING 0.40...</p>Probabilityhttps://gateoverflow.in/152362/gate-2016-maFri, 15 Sep 2017 10:48:10 +0000Probability doubt
https://gateoverflow.in/151117/probability-doubt
A box contains 10 red balls and 15 Blue Balls.One ball is lost. Two balls are drawn from box and are found to be red ones.Find the chance that the missing ball is blue ball.<br />
<br />
a)15/23<br />
<br />
b)0.347<br />
<br />
c)0.6<br />
<br />
d)noneProbabilityhttps://gateoverflow.in/151117/probability-doubtSun, 10 Sep 2017 04:53:48 +0000Expectation
https://gateoverflow.in/150904/expectation
Let A[1:n] be an array such that A[i]=i . An algorithm randomly permutes the elements of A, call the resulting array A' . Let X denote the number of location such that A'[i]=i. What is expectation of X?Probabilityhttps://gateoverflow.in/150904/expectationSat, 09 Sep 2017 09:30:56 +0000Normal Distribution
https://gateoverflow.in/150896/normal-distribution
The median of a normal variate x with probablity dessity function<br />
<br />
f(x) = 1/(sigma*root(2*pi)*exp[-{(x-u)^2}/(2*sigma^2)] = ?Probabilityhttps://gateoverflow.in/150896/normal-distributionSat, 09 Sep 2017 08:56:07 +0000