1
GATE CSE 1999
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
$${\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}$$
D
1/3
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