1
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
When a coin is tossed, the probability of getting a Head is p, 0 < p < 1. Let N be the random variable denoting the number of tosses till the first Head appears, including the toss where the Head appears. Assuming that successive tosses are indepandent, the expected value of N is
A
1/p
B
1/ (1 - p)
C
$$1/{p^2}$$
D
$$1/{(1 - p)^2}$$
2
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Box P has 2 red balls and 3 blue balls and box Q has 3 red balls and 1 blue ball. A ball is selected as follows: (i) select a box (ii) choose a ball from the selected box such that each ball in the box is equally likely to be chosen. The probabilities of selecting boxes P and Q are 1/3 and 2/3, respectively. Given that a ball selected in the above process is a red ball, the probability that it came from the box P is:
A
4/19
B
5/19
C
2/9
D
19/30
3
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
4
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
$$1 - \,\,{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle {{2^n}}$}}$$
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