Three dice are thrown simultaneously. What is the probability of obtaining a total of $17$ or $18$?

Let $E_1, E_2, E_3$ be three arbitrary events of a sample space $S$. Which of the following statements is correct?

$A$ 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 $p(w_3)$.

$A$ bag contains $3$ white,$3$ black and $2$ red balls. Three balls are drawn one by one without replacement. The probability that the third ball is red is:

Two dice are rolled. If both dice have six faces numbered $1, 2, 3, 5, 7, 11$,then the probability that the sum of the numbers on the uppermost faces is a prime number is:

$A$ coin is tossed twice. The probability of getting head both the times is