GATE FORUM - Recent questions and answers in Probability
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Powered by Question2AnswerAnswered: probability that the face value exceeds
http://gateforum.org//1628/probability-that-the-face-value-exceeds?show=2306#a2306
<p>Ans, 0.468</p><p></p><p>Let P<sub>n </sub>be the probability of corresponding face value occurence.</p><p>Total probability</p><p>P<sub>1</sub> + P<sub>2</sub> + P<span style="font-size:10.8333px; line-height:17.3333px">3</span> + P<sub>4</sub> + P<sub>5</sub> + P<sub>6</sub> = 1 .......... Eq. 1</p><p>According to conditions,</p><p>P<sub>1</sub> + P<span style="font-size:10.8333px">3</span> + P<sub>5 </sub>= 0.9( P<sub>2 </sub>+ P<sub>4</sub> + P<sub>6 </sub>) ............... Eq. 2</p><p>P<sub>4</sub> + P<sub>6 </sub>= 0.75( P<sub>4</sub> + P<sub>5</sub> + P<sub>6</sub> ) ..................... Eq. 3</p><p>but P<sub>2 </sub>= P<sub>4</sub> = P<sub>6 </sub>= P given</p><p>So Eq, 1 P<sub>1</sub> + P<span style="font-size:10.8333px">3</span> + P<sub>5 </sub>= 1 - 3P<sub>2</sub></p><p>Eq. 2 P<sub>1</sub> + P<span style="font-size:10.8333px">3</span> + P<sub>5 </sub>= 0.9 * 3P<sub>2</sub></p><p>Soving these, P<sub>2 </sub>= P<sub>4</sub> = P<sub>6 </sub>= P = 0.1754</p><p>Putting it in Eq. 3 P<sub>4</sub> + P<sub>5</sub> + P<sub>6</sub> = 0.468</p><p></p>Probabilityhttp://gateforum.org//1628/probability-that-the-face-value-exceeds?show=2306#a2306Wed, 10 Aug 2016 12:19:44 +0000Answered: probability that the sum of the two numbers equals
http://gateforum.org//1653/probability-that-the-sum-of-the-two-numbers-equals?show=1654#a1654
<pre>Probability = Favorable Outcomes/Total Outcomes
Probability = 4/20 = 0.20
</pre>Probabilityhttp://gateforum.org//1653/probability-that-the-sum-of-the-two-numbers-equals?show=1654#a1654Sat, 20 Feb 2016 21:17:08 +0000events in a probability space satisfying the following constraints
http://gateforum.org//1652/events-in-a-probability-space-satisfying-the-following-constraints
<p>E1 and E2 are events in a probability space satisfying the following constraints:</p><pre>
Pr(E1) = Pr(E2)
Pr(EI U E2) = 1
E1 and E2 are independent </pre><p>The value of Pr(E1), the probability of the event E1 is</p><table><tbody><tr><td><p>A</p></td><td><p>0</p></td></tr><tr><td><p>B</p></td><td><p>1/4</p></td></tr><tr><td><p>C</p></td><td><p>1/2</p></td></tr><tr><td><p>D</p></td><td><p>1</p></td></tr></tbody></table>Probabilityhttp://gateforum.org//1652/events-in-a-probability-space-satisfying-the-following-constraintsSat, 20 Feb 2016 21:16:17 +0000Answered: probability that they all occurred on the same day
http://gateforum.org//1650/probability-that-they-all-occurred-on-the-same-day?show=1651#a1651
<p>Prob(all accidents on Monday) = 1/7<sup>7</sup>. Similarly for other 6 days. So total probability = 7 * 1/7<sup>7</sup> = 1/7<sup>6</sup>.</p>Probabilityhttp://gateforum.org//1650/probability-that-they-all-occurred-on-the-same-day?show=1651#a1651Sat, 20 Feb 2016 21:15:48 +0000Answered: probability that at least one head and one tail turn up
http://gateforum.org//1648/probability-that-at-least-one-head-and-one-tail-turn-up?show=1649#a1649
probability is (16-2)/16 = 7/8Probabilityhttp://gateforum.org//1648/probability-that-at-least-one-head-and-one-tail-turn-up?show=1649#a1649Sat, 20 Feb 2016 21:14:59 +0000Answered: probability of the event
http://gateforum.org//1646/probability-of-the-event?show=1647#a1647
P(A | B) is Probability of A given B has occurred which is 1. P(B | A) is probability of B given that A has occurred which is 1/2Probabilityhttp://gateforum.org//1646/probability-of-the-event?show=1647#a1647Sat, 20 Feb 2016 21:14:19 +0000Answered: sum total of the expected marks obtained by all these students is
http://gateforum.org//1644/sum-total-of-the-expected-marks-obtained-by-all-these-students-is?show=1645#a1645
<pre>expected marks = 150*1000/16 = 9375</pre>Probabilityhttp://gateforum.org//1644/sum-total-of-the-expected-marks-obtained-by-all-these-students-is?show=1645#a1645Sat, 20 Feb 2016 21:13:23 +0000Answered: probability that two heads and two tails will result
http://gateforum.org//1642/probability-that-two-heads-and-two-tails-will-result?show=1643#a1643
probability of 2 heads is 6/16 which is 3/8Probabilityhttp://gateforum.org//1642/probability-that-two-heads-and-two-tails-will-result?show=1643#a1643Sat, 20 Feb 2016 21:12:42 +0000Answered: maximum value of P(A)P(B)
http://gateforum.org//1640/maximum-value-of-p-a-p-b?show=1641#a1641
P(A).P(B) = 1 /4 = 0.25Probabilityhttp://gateforum.org//1640/maximum-value-of-p-a-p-b?show=1641#a1641Sat, 20 Feb 2016 21:11:32 +0000Answered: probability that a given positive integer lying between 1 and 100 (both inclusive) is NOT divisible by 2, 3 or 5 is
http://gateforum.org//1638/probability-that-given-positive-integer-lying-between-and-100-both-inclusive-not-divisible-or?show=1639#a1639
probability that a number is number is not divisible by 2, 3 and 5 = (100 - 74)/100 = 0.25Probabilityhttp://gateforum.org//1638/probability-that-given-positive-integer-lying-between-and-100-both-inclusive-not-divisible-or?show=1639#a1639Sat, 20 Feb 2016 21:10:53 +0000expected length of the word drawn is
http://gateforum.org//1637/expected-length-of-the-word-drawn-is
<p>Each of the nine words in the sentence <strong>”The quick brown fox jumps over the lazy dog”</strong> is written on a separate piece of paper. These nine pieces of paper are kept in a box. One of the pieces is drawn at random from the box. The expected length of the word drawn is _____________.</p>Probabilityhttp://gateforum.org//1637/expected-length-of-the-word-drawn-isSat, 20 Feb 2016 21:10:00 +0000Answered: six-sided dice are rolled. The probability that the sum being 22 is X/1296. The value of X
http://gateforum.org//1635/six-sided-dice-are-rolled-the-probability-that-the-sum-being-22-is-x-1296-the-value-of-x?show=1636#a1636
probability = 10/1296Probabilityhttp://gateforum.org//1635/six-sided-dice-are-rolled-the-probability-that-the-sum-being-22-is-x-1296-the-value-of-x?show=1636#a1636Sat, 20 Feb 2016 21:08:13 +0000Answered: expected value of the smallest number in sample
http://gateforum.org//1633/expected-value-of-the-smallest-number-in-sample?show=1634#a1634
E = (1/(2^1))*(2^1) + (1/(2^2))*(2^2) + … (1/(2^n))*(2^n) = 1+1+…1 (n times addition of 1) = nProbabilityhttp://gateforum.org//1633/expected-value-of-the-smallest-number-in-sample?show=1634#a1634Sat, 20 Feb 2016 21:06:36 +0000Answered: probability that 2 appears at an earlier position than any other even number in the selected permutation
http://gateforum.org//1631/probability-that-appears-earlier-position-than-any-other-even-number-the-selected-permutation?show=1632#a1632
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Node of the aboveProbabilityhttp://gateforum.org//1631/probability-that-appears-earlier-position-than-any-other-even-number-the-selected-permutation?show=1632#a1632Sat, 20 Feb 2016 21:06:01 +0000random variable following normal distribution with mean +1 and variance
http://gateforum.org//1630/random-variable-following-normal-distribution-with-mean-1-and-variance
Let X be a random variable following normal distribution with mean +1 and variance 4. Let Y be another normal variable with mean -1 and variance unknown If P(X <=-1) = P(Y >-2). the standard deviation of Y isProbabilityhttp://gateforum.org//1630/random-variable-following-normal-distribution-with-mean-1-and-varianceSat, 20 Feb 2016 21:05:00 +0000probability that she studies computer science on Wednesday
http://gateforum.org//1629/probability-that-she-studies-computer-science-on-wednesday
Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that she studies mathematics the next day is 0.6. If she studies mathematics on a day, then the probability that she studies computer science the next day is 0.4. Given that Aishwarya studies computer science on Monday, what is the probability that she studies computer science on Wednesday?Probabilityhttp://gateforum.org//1629/probability-that-she-studies-computer-science-on-wednesdaySat, 20 Feb 2016 21:03:51 +0000Answered: probability that divisor of 1099 is a multiple of 1096
http://gateforum.org//1626/probability-that-divisor-of-1099-is-a-multiple-of-1096?show=1627#a1627
probability = 16/10000=1/625Probabilityhttp://gateforum.org//1626/probability-that-divisor-of-1099-is-a-multiple-of-1096?show=1627#a1627Sat, 20 Feb 2016 21:02:29 +0000Answered: probability of a computer being declared faulty
http://gateforum.org//1624/probability-of-a-computer-being-declared-faulty?show=1625#a1625
<table><tbody><tr><td><p>pq + (1 - p)(1 - q)</p></td></tr></tbody></table>Probabilityhttp://gateforum.org//1624/probability-of-a-computer-being-declared-faulty?show=1625#a1625Sat, 20 Feb 2016 21:01:43 +0000Answered: Two cards are then removed one at time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number on the second card
http://gateforum.org//1622/cards-removed-deck-probability-cards-selected-with-number-first-card-being-higher-number-second?show=1623#a1623
probability = 4/20 = 1/5Probabilityhttp://gateforum.org//1622/cards-removed-deck-probability-cards-selected-with-number-first-card-being-higher-number-second?show=1623#a1623Sat, 20 Feb 2016 21:00:56 +0000Answered: Which one of the following statements is INCORRECT
http://gateforum.org//1620/which-one-of-the-following-statements-is-incorrect?show=1621#a1621
<p>D</p><p><em>σ</em><sub><em>y</em></sub><em> = aσ</em><sub><em>x</em></sub><em>+b</em></p>Probabilityhttp://gateforum.org//1620/which-one-of-the-following-statements-is-incorrect?show=1621#a1621Sat, 20 Feb 2016 20:59:57 +0000Answered: difference between expectation of the square of a random variable (E[X²]) and the square of the expectation of the random variable (E[X])² is denoted by R
http://gateforum.org//1618/difference-between-expectation-square-variable-square-expectation-random-variable-denoted?show=1619#a1619
C<br />
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R >= 0Probabilityhttp://gateforum.org//1618/difference-between-expectation-square-variable-square-expectation-random-variable-denoted?show=1619#a1619Sat, 20 Feb 2016 20:59:10 +0000Answered: two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads
http://gateforum.org//1616/two-fair-coins-are-flipped-least-outcomes-known-head-what-probability-that-both-outcomes-heads?show=1617#a1617
one outcome is head, there are only three possibilities {h, t}, {h, h}, {t, h} The probability of both heads = 1/3Probabilityhttp://gateforum.org//1616/two-fair-coins-are-flipped-least-outcomes-known-head-what-probability-that-both-outcomes-heads?show=1617#a1617Sat, 20 Feb 2016 20:58:00 +0000Answered: random variable X that takes values +1 and −1 with probability 0.5 each. The values of the cumulative distribution function
http://gateforum.org//1614/random-variable-takes-values-with-probability-each-values-cumulative-distribution-function?show=1615#a1615
C<br />
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0.5 and 1Probabilityhttp://gateforum.org//1614/random-variable-takes-values-with-probability-each-values-cumulative-distribution-function?show=1615#a1615Sat, 20 Feb 2016 20:57:02 +0000Answered: fair six-sided die is rolled once probability that the sum total of values that turn up is at least
http://gateforum.org//1612/fair-six-sided-die-is-rolled-once-probability-that-the-sum-total-of-values-that-turn-up-is-at-least?show=1613#a1613
probability is 9/36 + 1/6 = 15/36 = 5/12Probabilityhttp://gateforum.org//1612/fair-six-sided-die-is-rolled-once-probability-that-the-sum-total-of-values-that-turn-up-is-at-least?show=1613#a1613Sat, 20 Feb 2016 20:56:08 +0000Answered: What is the probability that the selected number is not divisible by
http://gateforum.org//1610/what-is-the-probability-that-the-selected-number-is-not-divisible-by?show=1611#a1611
There are total 90 two digit numbers, out of them 13 are divisible by 7Probabilityhttp://gateforum.org//1610/what-is-the-probability-that-the-selected-number-is-not-divisible-by?show=1611#a1611Sat, 20 Feb 2016 20:55:09 +0000Answered: probability of observing fewer than 3 cars during any given minute in this interval
http://gateforum.org//1608/probability-of-observing-fewer-than-3-cars-during-any-given-minute-in-this-interval?show=1609#a1609
<p>C</p><p>17 / (2e<sup>3</sup>)</p>Probabilityhttp://gateforum.org//1608/probability-of-observing-fewer-than-3-cars-during-any-given-minute-in-this-interval?show=1609#a1609Sat, 20 Feb 2016 20:54:04 +0000