For any two events $A$ and $B$,if $P(A \cup B) = a P(A \cap B) + b P(A) + c P(B)$,then $3a + 2b + 5c = ?$

$A$ die is thrown. Let $A$ be the event that the number obtained is greater than $3$. Let $B$ be the event that the number obtained is less than $5$. Then $P(A \cup B)$ is

If the odds against $A$ solving a problem are $4:3$ and the odds in favor of $B$ solving the problem are $7:5$,what is the probability that only one of them solves the problem?

$A$ coin is tossed twice. If events $A$ and $B$ are defined as: $A = \text{head on first toss}$,$B = \text{head on second toss}$. Then the probability of $A \cup B = $

If the odds in favour of an event be $3 : 5$,then the probability of non-occurrence of the event is

In an entrance test that is graded on the basis of two examinations,the probability of a randomly chosen student passing the first examination is $0.8$ and the probability of passing the second examination is $0.7$. The probability of passing at least one of them is $0.95$. What is the probability of passing both?