When three coins are tossed simultaneously,what is the probability of getting at least one head?

$A$ die marked $1, 2, 3$ in red and $4, 5, 6$ in green is tossed. Let $A$ be the event 'the number is even' and $B$ be the event 'the number is red'. Are $A$ and $B$ independent?

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 $5$?

There are four men and six women on the city council. If one council member is selected for a committee at random,what is the probability that the selected member is a woman (in $/5$)?

$A$ 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 $p(w_3)$.

$A$ manager decides to distribute $Rs. 20000$ between two employees $X$ and $Y$. He knows $X$ deserves more than $Y$,but does not know how much more. So,he decides to arbitrarily break $Rs. 20000$ into two parts and gives $X$ the bigger part. Then,the chance that $X$ gets twice as much as $Y$ or more is