$A$ and $B$ are two events such that $P(A)=0.54$,$P(B)=0.69$ and $P(A \cap B)=0.35$. Find $P(B \cap A^{\prime})$.

Let $S$ be the sample space of the random experiment of throwing simultaneously two unbiased dice and $E_k = \{(a, b) \in S : ab = k\}$. If $p_k = P(E_k)$, then which of the following is correct?

If $A$ and $B$ are two events with $P(A \cup B) = 0.65$ and $P(A \cap B) = 0.15$,then find the value of $P(A^C) + P(B^C)$.

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

$A$ 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

$A$ mathematics problem is given to three students $A, B$,and $C$. The probabilities of them solving the problem are $1/2, 1/3$,and $1/4$ respectively. What is the probability that the problem is solved?