The probabilities of `A`, `B` and `C` solving a problem independently are respectively `(1)/(4)`, `(1)/(5)`, `(1)/(6)`. If `21` such problems are given to `A`, `B` and `C` then the probability that at least `11` problems can be solved by them is

Options

A. A. `"^(21)C_(11)((1)/(2))^(11)`
B. B. `(1)/(2)`
C. C. `((1)/(2))^(11)`
D. D. none of these

Answer

B

Explanation

`(b)` No. of trials `n=21`
Success in solving the problem
`:.p=P(AuuBuuC)=1-P(barA)P(barB)P(barC)`
`=1-(3)/(4)xx(4)/(5)xx(5)/(6)=(1)/(2)`
`:.q=(1)/(2)`
`:.` Required probability `P(X ge 11)=(1)/(2)`