1
GATE CSE 1999
+2
-0.6
Let X and Y be two exponentially distributed and independent random variables with mean $$\alpha$$ and $$\beta$$, respectively. If Z = min (X, Y), then the mean of Z is given by
A
$${1 \over {\alpha + \beta }}$$
B
$$\min \,(\alpha ,\,\beta )$$
C
$${{\alpha \,\beta } \over {\alpha + \beta }}$$
D
$${\alpha + \beta }$$
2
GATE CSE 1999
+2
-0.6
Consider two events $${{E_1}}$$ and $${{E_2}}$$ such that probability of $${{E_1}}$$, Pr [$${{E_1}}$$] = 1/2, probability of $${{E_2}}$$, Pr[$${{E_2}}$$ = 1/3, and probability of $${{E_1}}$$ and $${{E_2}}$$, $$\left[ {{E_1}\,\,or\,\,{E_2}} \right]$$ = 1/5. Which of the following statements is /are true?
A
$$\Pr \,\left[ {{E_1}\,\,or\,\,{E_2}} \right]$$ is 2/3
B
Events $${{E_1}}$$ and $${{E_2}}$$ are independent
C
Events $${{E_1}}$$ and $${{E_2}}$$ are not independent
D
$$\Pr \,\left[ {{E_1}\,/\,{E_2}} \right] = 4/5$$
3
GATE CSE 1996
+2
-0.6
The probability that the top and bottom cards of a randomly shuffled deck are both access is
A
$${4 \over {52}}\, \times \,{4 \over {52}}\,$$
B
$${4 \over {52}}\, \times \,{3 \over {52}}\,$$
C
$${4 \over {52}}\, \times \,{3 \over {51}}\,$$
D
$${4 \over {52}}\, \times \,{4 \over {51}}\,$$
4
GATE CSE 1995
+2
-0.6
A bag contains 10 white balls and 15 black balls. Two balls drawn in succession. The probability that one of them is black the other is white is
A
2/3
B
4/5
C
$${\raise0.5ex\hbox{1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{2}}$$
D
1/3
GATE CSE Subjects
Theory of Computation
Operating Systems
Algorithms
Digital Logic
Database Management System
Data Structures
Computer Networks
Software Engineering
Compiler Design
Web Technologies
General Aptitude
Discrete Mathematics
Programming Languages
Computer Organization
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