The odds in favour of getting a sum that is a multiple of $3$,when a pair of dice is thrown,is:

It is $5:2$ against a husband who is $65$ years old living till he is $85$ and $4:3$ against his wife who is now $58$,living till she is $78$. If the probability that at least one of them will be alive for $20$ years is $k$,then the value of $49k$ is:

The probabilities of occurrence of two events are respectively $0.21$ and $0.49$. The probability that both occur simultaneously is $0.16$. Then the probability that none of the two occurs is

Three ships $A$, $B$, and $C$ sail from England to India. If the odds in favour of their safe arrival are $2:5$, $3:7$, and $6:11$ respectively, then the probability that exactly two ships arrive safely is

There are three events $A, B, C$,one of which must and only one can happen. The odds are $8:3$ against $A$,$5:2$ against $B$,and the odds against $C$ are $43:17k$. Then the value of $k$ is:

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 the events $A$ and $B$ are independent.