Six faces of an unbiased die are numbered with $2,3,5,7,11$ and 13 . If two such dice are thrown, then the…
Six faces of an unbiased die are numbered with $2,3,5,7,11$ and 13 . If two such dice are thrown, then the probability that the sum on the uppermost faces of the dice is an odd number is
$\frac{5}{18}$
$\frac{5}{36}$
$\frac{13}{18}$
$\frac{25}{36}$
Solution
The sum of two numbered on a dice is odd only, whence once is odd and second is even.
$\therefore$ Required probability
$=2 \times$ Probability of odd number $\times$ Probability of even number
[ $\because$ Here, we multiply by 2 because either the even number is on first or second dice.]
$
=2 \times\left(\frac{5}{6}\right) \times\left(\frac{1}{6}\right)=\frac{5}{18}
$