GATE CSE 2008 | Probability Question 38 | Discrete Mathematics

GATE CSE 2008

MCQ (Single Correct Answer)

-0.6

Let X be a random variable following normal distribution with mean + 1 and variance 4. Let Y be another normal variable with mean - 1 and variance unknown. If $$P\,(X\, \le \, - 1) = \,P(Y\,\, \ge \,2)$$, the standard deviation of Y is

$${\sqrt 2 }$$

GATE CSE 2008

MCQ (Single Correct Answer)

-0.6

What is the probability that in a randomly choosen group of r people at least three people have the same birthday?

$$1 - {{365.364....\,(365\, - \,r\, + \,1)} \over {{{365}^r}}}$$

$$ {{365.364....\,(365\, - \,r\, + \,1)} \over {{{365}^r}}}$$
$$ + {\,^r}{C_2}.\,365.{{364.363....\,(364\, - \,(r - 2)\, + \,1)} \over {{{365}^{r - 2}}}}$$

$$1 - {{365.364....\,(365\, - \,r\, + \,1)} \over {{{365}^r}}}$$
$$ - {\,^r}{C_2}.\,365.{{364.363....\,(364\, - \,(r - 2)\, + \,1)} \over {{{365}^{r - 2}}}}$$

$${{365.364....\,(365\, - \,r\, + \,1)} \over {{{365}^r}}}$$

GATE CSE 2007

MCQ (Single Correct Answer)

-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?

$${{1 \over 2}}$$

$${{1 \over 10}}$$

$${{9! \over 20!}}$$

None of the above.

GATE CSE 2006

MCQ (Single Correct Answer)

-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

1/p

1/ (1 - p)

$$1/{p^2}$$

$$1/{(1 - p)^2}$$

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