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 $p(w_3)$.

Three persons $P, Q$ and $R$ independently try to hit a target. If the probabilities of their hitting the target are $\frac{3}{4}, \frac{1}{2}$ and $\frac{5}{8}$ respectively,then the probability that the target is hit by $P$ or $Q$ but not by $R$ is

Let $A, B$ and $C$ be three events associated with sample space $S$. $A, B$ and $C$ are pairwise independent and $P(A)=P(B)=P(C)=P$. If all of them cannot occur simultaneously,then $P(A \cup B \cup C)$ is equal to

$A$ set $S$ contains $7$ elements. $A$ non-empty subset $A$ of $S$ and an element $x$ of $S$ are chosen at random. Then the probability that $x \in A$ is

Which of the following cannot be a valid assignment of probabilities for outcomes of sample space $S = \{\omega_{1}, \omega_{2}, \omega_{3}, \omega_{4}, \omega_{5}, \omega_{6}, \omega_{7}\}$?

Outcome	Probability
$\omega_{1}$	$\frac{1}{14}$
$\omega_{2}$	$\frac{2}{14}$
$\omega_{3}$	$\frac{3}{14}$
$\omega_{4}$	$\frac{4}{14}$
$\omega_{5}$	$\frac{5}{14}$
$\omega_{6}$	$\frac{6}{14}$
$\omega_{7}$	$\frac{15}{14}$