In a series of n independent trials for an event of consist probability p, the most probable number r of successes is given by `(n+1)p-1 lt r lt (n+1)p`.
Hence the most probable number of successes is the integral part of `(n+1)` p, But if `(n+1)` p is an integer the chance of r successes is equal to that of `(r+1)` successes and bot r,r+1 are most problem number of successes.
A bag contains 2 white and 1 black balls. A ball is drawn at random and returned to bag.
The experiment is done 10 times. The probability that a white ball is drawn exactly 5 times is .

Options

A. `(10!)/(5!5!)((2)/(3))^5`
B. `(10!)/(5!5!)((1)/(3))^5`
C. `(10!)/((5)^2)((2)/(9))^5`
D. `(10!)/(5!)((2)/(9))^5`.

Answer

C