A coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows $6$ is

Two dice are thrown. The probability that the sum of the points on two dice will be $7$, is

Let $\quad S =\left\{ M =\left[ a _{ ij }\right], a _{ ij } \in\{0,1,2\}, 1 \leq i , j \leq 2\right\}$ be a sample space and $A=\{M \in S: M$ is invertible $\}$ be an event. Then $P ( A )$ is equal to

A bag contains $5$ white, $7$ red and $8$ black balls. If four balls are drawn one by one without replacement, what is the probability that all are white

A determinant is chosen at random from the set of all determinants of order $2$ with elements $0$ or $1$ only. The probability that the determinant chosen is non-zero is