1
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the tails are independent, the expected number of tosses are
A
3
B
4
C
5
D
6
2
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on outcomes head and tail, respectively. The probability that two such randomly generated strings are not identical is:
A
$$1/{2^n}$$
B
1 - 1/n
C
1/n!
D
$$1 - \,\,{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle {{2^n}}$}}$$
3
GATE CSE 2004
MCQ (Single Correct Answer)
+2
-0.6
A point is randomly selected with uniform probability in the X-Y plane within the rectangle with corners at
(0, 0), (1, 0), (1, 2) and (0, 2). If p is the length of the position vector of the point, the expected value of $${p^2}$$ is
A
2/3
B
1
C
4/3
D
5/3
4
GATE CSE 2004
MCQ (Single Correct Answer)
+2
-0.6
An examination paper has 150 multiple-choice questions of one mark each, with each question having four choices. Each incorrect answer fetches-0.25 mark. Suppose 1000 students choose all their answers randomly with uniform probability. The sum total of the expected marks obtained all these students is
A
0
B
2550
C
7525
D
9375
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Graduate Aptitude Test in Engineering
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