Maharashtra Board Solutions for Chapter: Probability, Exercise 5: EXERCISE 9.5

If odds in favour of $X$ solving a problem are $4:3$ and odds against $Y$ solving the same problem are $2:3$. Find probability of $X$ solving the problem.

The odds against student $X$ solving a statistics problem are $8:6$ and odds in favour of student $Y$ solving the same problem are $14:16$. Find is the chance that the problem will be solved if they try it independently.

The odds against student $X$ solving a statistics problem are $8:6$ and odds in favour of student $Y$ solving the same problem are $14:16$. Find is the chance that neither of them solves the problem.

The odds against a husband who is $60$ years old, living till he is $85$ are $7:5$. The odds against his wife who is now $56$, living till she is $81$ are $5:3$. Find the probability that at least one of them will be alive $25$ years hence.

The odds against a husband who is $60$ years old, living till he is $85$ are $7:5$. The odds against his wife who is now $56$, living till she is $81$ are $5:3$. Find the probability that exactly one of them will be alive $25$ years hence.

There are three events $A, B$ and $C$, one of which must, and only one can happen. The odds against the event $A$ are $7:4$ and odds against event $B$ are $5:3$. Find the odds against event $C$.

In a single toss of a fair die, what are the odds against the event that number $3$ or $4$ turns up?

The odds in favour of $A$ winning a game of chess against $B$ are $3:2$. If three games are to be played, what are the odds in favour of $A\text{'}\mathrm{s}$ winning at least two games out of the three?