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

The probabilities of `A`, `B` and `C` solving a problem independently

1.	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 isA. `"^(21)C_(11)((1)/(2))^(11)`B. `(1)/(2)`C. `((1)/(2))^(11)`D. none of these
Answer» Correct Answer - B `(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)`

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