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
EXAM MAP
Medical
NEET