1
GATE CSE 2001
+2
-0.6
Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day ?
A
$$1/{7^7}$$
B
$$1/{7^6}$$
C
$$1/{2^7}$$
D
$$7/{2^7}$$
2
GATE CSE 2000
+2
-0.6
$${{E_1}}$$ and $${{E_2}}$$ are events in a probability space satisfying the following constraints:
$$\bullet$$ $$\Pr \,\,({E_1}) = \Pr \,({E_2})$$
$$\bullet$$ $$\Pr \,\,({E_1}\, \cup {E_2}) = 1$$
$$\bullet$$ $${E_1}$$ & $${E_2}$$ are independent

The value of Pr ($${E_1}$$), the probability of the event $${E_1}$$, is

A
0
B
1/4
C
1/2
D
1
3
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
$${\alpha + \beta }$$
4
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
$$\Pr \,\left[ {{E_1}\,/\,{E_2}} \right] = 4/5$$
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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