Subject-wise GATE questions
12 questions and papers
\(P\) 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…
Suppose \(Y\) is distributed uniformly in the open interval \((1,6)\). The probability that the polynomial \(3x^{2}+6xY+3Y+6\) has only real roots is (rounded off to 1 decimal place) ______.
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…
Suppose \(X_i\) for \(i=1,2,3\) are independent and identically distributed random variables whose probability mass functions are \(\Pr[X_i=0]=\Pr[X_i=1]=1/2\) for \(i=1,2,3\). Define another random variable \(Y=X_1X_2\oplus X_3\), where \(\oplus\) denotes XOR. Then…
Four fair six-sided dice are rolled. The probability of the sum of the results being 22 is \(\dfrac{X}{1296}\). The value of \(X\) is ______.
Suppose \(p\) is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and \(p\) has a Poisson distribution with…
Consider a random variable \(X\) that takes values \(+1\) and \(-1\) with probability \(0.5\) each. The values of the cumulative distribution function \(F(x)\) at \(x=-1\) and \(x=+1\) are
Consider a company that assembles computers. The probability of a faulty assembly of any computer is \(p\). The company therefore subjects each computer to a testing process. This…
An unbalanced die (with 6 faces, numbered from 1 to 6) is thrown. The probability that the face value is odd is \(90\%\) of the probability that the face value is even. The probability of getting any even numbered face is the same. If the probability that the face is even given that it is greater than 3 is \(0.75\), which one of the following…
For each element in a set of size \(2n\), an unbiased coin is tossed. The \(2n\) coin tosses are independent. An element is chosen if the corresponding coin…
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