If the odds against solving a question by three students are $2:1$,$5:2$,and $5:3$ respectively,then the probability that the question is solved by only one student is

If $A$ and $B$ are two independent events,then the probability of occurrence of at least one of $A$ and $B$ is given by $1 - P(A') P(B')$. Is this statement true or false?

The probability that a student will succeed in the $IIT$ entrance test is $0.2$ and the probability that he will succeed in the Roorkee entrance test is $0.5$. If the probability that he will be successful at both places is $0.3$,then the probability that he does not succeed at either place is:

Let $A$ and $B$ be two events such that $P(A) = 0.3$ and $P(A \cup B) = 0.8$. If $A$ and $B$ are independent events,then $P(B) = $

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

For an event,the odds against are $6 : 5$. The probability that the event does not occur is