GATE CSE 2008 | Probability Question 45 | Discrete Mathematics

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 2008

MCQ (Single Correct Answer)

-0.6

Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that the studies mathematics the next day is 0.6. If she studies mathematics on a day, then the probability that she studies computer science the next day is 0.4. Given that Aishwarya studies computer science on Monday, what is the probability that she studies computer science on Wednesday?

0.24

0.36

0.4

0.6

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 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.

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