Odds in Favor and Odds against an Event

Q.

A problem in statistics is given to four students A, B, C, and D. Their chances of solving it are$\frac{1}{3},\frac{1}{4},\frac{1}{5}$ and $\frac{1}{6}$ respectively. What is the probability that the problem will be solved?

1. $\frac{1}{3}$

2. $\frac{2}{3}$

3. $\frac{4}{5}$

4. None of these

Q. Three critics review a book. Odds in favour of th ebook are $5:2,4:3$ and $3:4$, respectively, for the three critics. The probability that majority are in favor off the book is

1. $\frac{35}{49}$
2. $\frac{125}{343}$
3. $\frac{164}{343}$
4. $\frac{209}{343}$

Q. The odds in favour of A solving a problem are 3 to 4 and the odds against B solving the same problem are 5 to 7. If they both try the problem, the probability that the problem is solved is:

1. $\frac{41}{84}$
2. $\frac{16}{21}$
3. $\frac{5}{21}$
4. $\frac{1}{4}$

Q. A point is selected at random inside an equilateral triangle whose side length is $3$ units. If the probability that its distance from any corner of the triangle is greater than $1$ unit is $1-\frac{2\pi }{k\sqrt{3}}$, then $k$ is

Q. A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn one-by-one with replacement, then the variance of the number of green balls drawn is ?

1. $\frac{12}{5}$
2. $6$
3. $4$
4. $\frac{6}{25}$

Q. Three critics review a book. Odds in favour of th ebook are $5:2,4:3$ and $3:4$, respectively, for the three critics. The probability that majority are in favor off the book is

1. $\frac{35}{49}$
2. $\frac{125}{343}$
3. $\frac{164}{343}$
4. $\frac{209}{343}$