When two dice are thrown simultaneously,what is the probability that at least one of the dice shows a number greater than $3$?

$A$ student appears for tests $I, II$ and $III$. The student is successful if he passes either in tests $I$ and $II$ or tests $I$ and $III$. The probabilities of the student passing in tests $I, II, III$ are $p, q$ and $\frac{1}{2}$ respectively. If the probability that the student is successful is $\frac{1}{2}$,then

$A$ random experiment has five outcomes $w_1, w_2, w_3, w_4$ and $w_5$. The probabilities of the occurrence of the outcomes $w_1, w_2, w_3, w_4$ and $w_5$ are respectively $\frac{1}{6}, a, b, c$ and $\frac{1}{12}$ such that $12a + 12b - 1 = 0$. If $p(w_4) = c$ and the outcomes are equally likely for $w_2, w_3, w_4$,find the probability of the outcome $w_3$. Given the condition $12a + 12b = 1$,and assuming $a=b=c$ for the remaining outcomes,find $p(w_3)$.

The vertices of a regular tetrahedron are marked $1, 2, 3, 4$. If three such tetrahedra are thrown simultaneously,what is the probability that the sum of the numbers on the faces is $5$?

If the roots of each of the equations $2x^2+x-1=0$,$3x^2-10x+3=0$,and $6x^2+11x-2=0$ correspond to probabilities of three events of a random experiment,then those events are

$A$ bag contains $6$ white,$5$ black,and $4$ red balls. Find the probability of getting a white or a black ball when one ball is drawn from the bag.