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Ques 21 GATE 2014
10% of the population in a town is HIV+. A new diagnostic kit for HIV detection is available; this kit correctly identifies HIV+ individuals 95% of the time, and HIV− individuals 89% 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 _______
(0.48) is the correct answer.
Ques 22 GATE 2014
In any given year, the probability of an earthquake greater than Magnitude 6 occurring in the Garhwal Himalayas is 0.04. The average time between successive occurrences of such earthquakes is _______ years.
(25 to 25) is the correct answer.
Ques 23 GATE 2014
10% of the population in a town is HIV⁺. A new diagnostic kit for HIV detection is available; this kit correctly identifies HIV⁺ individuals 95% of the time, and HIV individuals 89% 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
(0.48 to 0.49) is the correct answer.
Ques 24 GATE 2013
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?
(b) is the correct answer.
Ques 25 GATE 2013
For two rolls of a fair die, the probability of getting a 4 in the first roll and a number less than 4 in the second roll, up to 3 digits after the decimal point, is
(0.167) is the correct answer.
Ques 26 GATE 2013
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?
(c) is the correct answer.
Ques 27 GATE 2012
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 shock absorbers, 96% are reliable. Of Y's shock absorbers, 72% are reliable. The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is
(b) is the correct answer.
Ques 28 GATE 2012
A smuggler has 10 capsules in which five are filled with narcotic drugs and the rest contain the original medicine. All the 10 capsules are mixed in a single box, from which the customs officials picked two capsules at random and tested for the presence of narcotic drugs. The probability that the smuggler will be caught is
(c) is the correct answer.