In a college, $40 \%$ of students attend the Mathematics class, $30 \%$ of students attend the Physics class, and $20 \%$ of students attend both classes. If a student is chosen at random from the college, what is the probability that the chosen student attends only one class?

If the events $A$ and $B$ are independent,and $P(A^{\prime}) = \frac{2}{3}$ and $P(B^{\prime}) = \frac{2}{7}$,then $P(A \cap B)$ is equal to:

$A$ die is thrown. Find the probability of the following event: $A$ number more than $6$ will appear.

$A$ problem in Algebra is given to two students $A$ and $B$ whose chances of solving it are $\frac{2}{5}$ and $\frac{3}{4}$ respectively. The probability that the problem is solved, if both of them try independently, is

$A$ 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 $p(w_3)$.

$A$ container holds two balls. Both balls are black. If one white ball is added to the container and then one ball is drawn at random from the container,what is the probability that it is white?