Given that the events $A$ and $B$ are such that $P(A)=\frac{1}{2}, P(A \cup B)=\frac{3}{5}$ and $P(B)=p .$ Find $p$ if they are independent.
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 neither $NCC$ nor $NSS$.
Twelve tickets are numbered $1$ to $12$. One ticket is drawn at random, then the probability of the number to be divisible by $2$ or $3$, is
Let ${E_1},{E_2},{E_3}$ be three arbitrary events of a sample space $S$. Consider the following statements which of the following statements are correct
If $P(A) = 2/3$, $P(B) = 1/2$ and ${\rm{ }}P(A \cup B) = 5/6$ then events $A$ and $B$ are