1
GATE CSE 2007
+2
-0.6
Suppose we uniformly and randomly select a permutation from the 20! permutations of 1, 2, 3,..., 20. What is the promutations that 2 appears at an earlier position than any other even number in the selected permutation?
A
$${{1 \over 2}}$$
B
$${{1 \over 10}}$$
C
$${{9! \over 20!}}$$
D
None of the above.
2
GATE CSE 2006
+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
$$1/{(1 - p)^2}$$
3
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
4
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
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