1
GATE CSE 2005
+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
2
GATE CSE 2005
+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
3
GATE CSE 2005
+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
$$1 - \,\,{\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle {{2^n}}}}$$
4
GATE CSE 2004
+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
GATE CSE Subjects
EXAM MAP
Medical
NEET