Let $A$ and $B$ be two events such that $P(A') = 0.3$,$P(B) = 0.4$,and $P(A \cap B') = 0.5$. Then $P(A \cup B')$ is:

One card is selected at random from $27$ cards numbered from $1$ to $27$. What is the probability that the number on the card is even or divisible by $5$?

Let $A$ and $B$ be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ and the probability that $A$ or $B$ occurs is $\frac{1}{2}$. Then,the probability that both of them occur together is:

$A$ bag contains $5$ black balls, $4$ white balls and $3$ red balls. If a ball is selected at random, the probability that it is a black or a red ball, is

$A$ batch of pencils contains $12$ good,$6$ slightly defective,and $2$ very defective pencils. If a pencil is selected at random,what is the probability that it is a non-defective pencil?

In a class of $60$ students,$30$ opted for $NCC$,$32$ opted for $NSS$,and $24$ opted for both $NCC$ and $NSS$. If one of these students is selected at random,find the probability that the student has opted for $NSS$ but not $NCC$.