The probability that the sum of $2$ numbers chosen at random from $30$ consecutive integers is odd is..........

  • A
    $\frac{14}{29}$
  • B
    $\frac{16}{29}$
  • C
    $\frac{15}{29}$
  • D
    $\frac{10}{29}$

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Let $S$ be the set of all the words that can be formed by arranging all the letters of the word $\text{GARDEN}$. From the set $S$,one word is selected at random. The probability that the selected word will $\text{NOT}$ have vowels in alphabetical order is:

$A$ flashlight has $10$ batteries,out of which $4$ are dead. If $3$ batteries are selected without replacement and tested,then the probability that all $3$ are dead is:

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$A$ bag contains $4$ red, $3$ white, and $5$ blue balls. Three balls are drawn at a time randomly from the bag. Match the items from List-$I$ with those of List-$II$.
List-$I$List-$II$
$A$. Probability of getting $1$ red, $1$ white and $1$ blue ball$(i)$ $\frac{3}{44}$
$B$. Probability of getting $2$ white and $1$ blue ball$(ii)$ $\frac{21}{55}$
$C$. Probability of getting $2$ red and $1$ white ball$(iii)$ $\frac{38}{55}$
$D$. Probability that none of the balls is white$(iv)$ $\frac{3}{11}$
$(v)$ $\frac{9}{110}$

$A$ board has $16$ squares arranged in a $4 \times 4$ grid. Out of these $16$ squares,two squares are chosen at random. The probability that they have no side in common is:

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